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Séminaires et Congrès - Titles - 26 (2013) 253-279

Titles < 26

Operads 2009
VERSION IMPRIMEE A VENIR - PRINT VERSION NOT YET AVAILABLE
Loday, Jean-Louis and Vallette, Bruno, eds
Séminaires et Congrès 26 (2013), 281 pages
Presentation, Summary

The (non-equivariant) homology of the little disks operad
Dev P. Sinha
Séminaires et Congrès 26 (2013), 253-279

Résumé :
L'homologie (non équivariante) de l'opérade des petits disques
Dans cet article d'exposition, nous calculons explicitement et de manière élémentaire l'homologie de l'opérade des petits disques. Ceci implique que l'homologie d'un espace de lacets d fois itérés est une algèbre de Poisson. En démontrant ce résultat, nous cherchons à familiariser le lecteur avec les espaces de configurations de points dans un espace euclidien et ce en utilisant des outils élémentaires. Les nouveaux résultats portent sur l'identification de la dualité entre l'homologie et la cohomologie de ces espaces à l'aide d'une dualité entre certains graphes et arbres ainsi qu'en utilisant la structure de coopérade des groupes de cohomologie.

Abstract:
In this expository paper we give an elementary, explicit computation of the homology of the little disks operad, which then shows that the homology of a d-fold loop space is a Poisson algebra. In the course of proving this basic result, we aim to familiarize a larger audience with Euclidean configuration spaces, using elementary tools. New results include identifying the pairing between homology and cohomology of these spaces as a pairing of graphs and trees, and treating the cooperad structure on cohomology.

Keywords: Little disks operads, configurations spaces, Poisson (co)operad.

Class. math. : 18D50, 55P48, 55R80.


ISBN : 978-2-85629-363-8
ISSN : 1285-2783

Bibliographie:

1
Orlik, Peter and Solomon, Louis
Combinatorics and topology of complements of hyperplanes
Invent. Math. 56 (1980) 167–189
Math Reviews MR558866
2
Fadell, Edward and Neuwirth, Lee
Configuration spaces
Math. Scand. 10 (1962) 111-118
Math Reviews MR0141126
4
Chen, Weimin and Ruan, Yongbin
Orbifold Gromov-Witten theory
in Orbifolds in mathematics and physics (Madison, WI, 2001)
Contemp. Math. 310 (2002) 25–85
Math Reviews MR1950941
5
Grojnowski, I.
Instantons and affine algebras. I. The Hilbert scheme and vertex operators
Math. Res. Lett. 3 (1996) 275–291
Math Reviews MR1386846
6
Mui, Huynh
Modular invariant theory and cohomology algebras of symmetric groups
J. Fac. Sci. Univ. Tokyo Sect. IA Math. 22 (1975) 319–369
Math Reviews MR0422451
7
Chen, Kuo-Tsai and Fox, R. H. and Lyndon, R. C.
Free differential calculus. IV. The quotient groups of the lower central series
Ann. of Math. 68 (1958) 81–95
Math Reviews MR0102539
8
Sinha, Dev P. and Walter, Ben
Lie coalgebras and rational homotopy theory, I: graph coalgebras.
math.AT/0610437
9
Giusti, Chad and Salvatore, Paolo and Sinha, Dev P.
The mod 2 cohomology of symmetric groups as a Hopf ring over the Steenrod algebra
arXiv:0909.3292
10
Nishida, Goro
Cohomology operations in iterated loop spaces
Proc. Japan Acad. 44 (1968) 104–109
Math Reviews MR0240811
11
Bruner, R. R. and May, J. Peter and McClure, James E. and Steinberger, M.
H ring spectra and their applications
Lecture Notes in Math., vol. 1176, Springer, 1986
Math Reviews MR836132
12
Atiyah, M. F. and Segal, G. B.
Equivariant K-theory and completion
J. Differential Geometry 3 (1969) 1–18
Math Reviews MR0259946
13
Knutson, Donald
-rings and the representation theory of the symmetric group
Lecture Notes in Math., vol. 308, Springer, 1973
Math Reviews MR0364425
14
Zelevinsky, Andrey V.
Representations of finite classical groups
Lecture Notes in Math., vol. 869, Springer, 1981 A Hopf algebra approach
Math Reviews MR643482
15
Milgram, R. James
The mod2 spherical characteristic classes
Ann. of Math. 92 (1970) 238–261
Math Reviews MR0263100
16
Adem, José
The relations on Steenrod powers of cohomology classes. Algebraic geometry and topology
in A symposium in honor of S. Lefschetz
(1957) 191–238
Math Reviews MR0085502
17
Steenrod, N. E.
Homology groups of symmetric groups and reduced power operations
Proc. Nat. Acad. Sci. U. S. A. 39 (1953) 213–217
Math Reviews MR0054964
18
Ravenel, Douglas C. and Wilson, W. Stephen
The Hopf ring for complex cobordism
J. Pure Appl. Algebra 9 (1976/77) 241–280
Math Reviews MR0448337
19
Armstrong, M.A.
Basic Topology
Undergraduate Texts in Mathematics, Springer, 1983
20
Stanton, Dennis and White, Dennis
Constructive Combinatorics
Undergraduate Texts in Mathematics, Springer, 1986
21
Quillen, Daniel and Venkov, B. B.
Cohomology of finite groups and elementary abelian subgroups.
Topology 11 (1972) 317-318
22
Quillen, Daniel
The spectrum of an equivariant cohomology ring, I.
Ann. of Math. 94 (1971) 549–572.
23
Hu'ng, Nguyen Hũ'u Viet
The modulo 2 cohomology algebras of symmetric groups
Japan. J. Math. (N.S.) 13 (1987) 169–208
Math Reviews MR914318
24
Strickland, Neil P. and Turner, Paul R.
Rational Morava E-theory and DS0
Topology 36 (1997) 137–151
Math Reviews MR1410468
25
Strickland, Neil P.
Morava E-theory of symmetric groups
Topology 37 (1998) 757–779
Math Reviews MR1607736
26
Kudo, Tatsuji and Araki, Shôrô
Topology of Hn-spaces and H-squaring operations
Mem. Fac. Sci. Kyūsyū Univ. Ser. A. 10 (1956) 85–120
Math Reviews MR0087948
27
Reutenauer, Christophe
Free Lie algebras
London Mathematical Society Monographs. New Series, vol. 7, The Clarendon Press Oxford Univ. Press, 1993 Oxford Science Publications
Math Reviews MR1231799
28
Priddy, Stewart B.
Koszul resolutions
Trans. Amer. Math. Soc. 152 (1970) 39–60
Math Reviews MR0265437
29
Cartan, Henri and Serre, Jean-Pierre
Espaces fibrés et groupes d'homotopie. II. Applications
C. R. Acad. Sci. Paris 234 (1952) 393–395
Math Reviews MR0046046
30
Chevalley, Claude and Eilenberg, Samuel
Cohomology theory of Lie groups and Lie algebras
Trans. Amer. Math. Soc. 63 (1948) 85–124
Math Reviews MR0024908
31
Milgram, R. James
Iterated loop spaces
Ann. of Math. 84 (1966) 386–403
Math Reviews MR0206951
32
Carlsson, Gunnar and Milgram, R. James
Stable homotopy and iterated loop spaces
in Handbook of algebraic topology
(1995) 505–583
Math Reviews MR1361898
33
Hatcher, Allen
Algebraic topology
Cambridge Univ. Press, 2002
Math Reviews MR1867354
34
James, I. M.
Reduced product spaces
Ann. of Math. 62 (1955) 170–197
Math Reviews MR0073181
35
Moore, John C.
Differential homological algebra
in Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 1
(1971) 335–339
Math Reviews MR0436178
36
37
Abbaspour, Hossein and Chataur, David
On the homology of the space of singular knots.
arXiv:0901.0263
39
Vasilev, V. A.
Combinatorial computation of combinatorial formulas for knot invariants
Tr. Mosk. Mat. Obs. 66 (2005) 3–92
Math Reviews MR2193429
40
Tourtchine, Victor
On the other side of the bialgebra of chord diagrams
J. Knot Theory Ramifications 16 (2007) 575–629
Math Reviews MR2333307
41
Saneblidze, Samson and Umble, Ronald
Diagonals on the permutahedra, multiplihedra and associahedra
Homology Homotopy Appl. 6 (2004) 363–411
Math Reviews MR2118493
42
Goodwillie, Thomas G. and Klein, John R.
Multiple disjunction for spaces of Poincaré embeddings
J. Topol. 1 (2008) 761–803
Math Reviews MR2461855
43
Feichtner, Eva-Maria and Kozlov, Dmitry N.
Incidence combinatorics of resolutions
Selecta Math. (N.S.) 10 (2004) 37–60
Math Reviews MR2061222
44
Bisson, Terrence P. and Joyal, André
Q-rings and the homology of the symmetric groups
in Operads: Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995)
Contemp. Math. 202 (1997) 235–286
Math Reviews MR1436923
45
Loday, Jean-Louis
Cyclic homology
Grund. Math. Wiss., vol. 301, Springer, 1998 Appendix E by María O. Ronco, Chapter 13 by the author in collaboration with Teimuraz Pirashvili
Math Reviews MR1600246
46
Brown, Edgar H. Jr.
Twisted tensor products. I
Ann. of Math. 69 (1959) 223–246
Math Reviews MR0105687
47
Schlessinger, Michael and Stasheff, James
The Lie algebra structure of tangent cohomology and deformation theory
J. Pure Appl. Algebra 38 (1985) 313–322
Math Reviews MR814187
48
Goodwillie, Thomas G.
Calculus. III. Taylor series
Geom. Topol. 7 (2003) 645–711
Math Reviews MR2026544
49
Gómez-Tato, Antonio and Halperin, Stephen and Tanré, Daniel
Rational homotopy theory for non-simply connected spaces
Trans. Amer. Math. Soc. 352 (2000) 1493–1525
Math Reviews MR1653355
50
Brown, Edgar H. Jr. and Szczarba, Robert H.
Rational and real homotopy theory with arbitrary fundamental groups
Duke Math. J. 71 (1993) 299–316
Math Reviews MR1230293
51
Madsen, Ib and Milgram, R. James
The classifying spaces for surgery and cobordism of manifolds
Annals of Math. Studies, vol. 92, Princeton Univ. Press, 1979
Math Reviews MR548575
52
Hazewinkel, Michiel
Cofree coalgebras and multivariable recursiveness
J. Pure Appl. Algebra 183 (2003) 61–103
Math Reviews MR1992043
53
Block, Richard E. and Griffing, Gary
Recognizable formal series on trees and cofree coalgebraic systems
J. Algebra 215 (1999) 543–573
Math Reviews MR1686206
54
Block, Richard E.
Commutative Hopf algebras, Lie coalgebras, and divided powers
J. Algebra 96 (1985) 275–306
Math Reviews MR808852
55
Barr, Michael
Harrison homology, Hochschild homology and triples
J. Algebra 8 (1968) 314–323
Math Reviews MR0220799
56
Vallette, Bruno
A Koszul duality for PROPs
Trans. Amer. Math. Soc. 359 (2007) 4865–4943
Math Reviews MR2320654
57
Curtis, Edward B.
The Dyer-Lashof algebra and the -algebra
Illinois J. Math. 19 (1975) 231–246
Math Reviews MR0377885
58
Mandell, Michael A.
Cochains and homotopy type
Publ. Math. Inst. Hautes Études Sci. (2006) 213–246
Math Reviews MR2233853
59
Johnson, Brenda
The derivatives of homotopy theory
Trans. Amer. Math. Soc. 347 (1995) 1295–1321
Math Reviews MR1297532
60
Livernet, Muriel
On a plus-construction for algebras over an operad
K-Theory 18 (1999) 317–337
Math Reviews MR1738897
61
Spitzweck, Markus
Operads, algebas and modules in general model categories.
math.AT/0101102
62
Hinich, Vladimir
Homological algebra of homotopy algebras
Comm. Algebra 25 (1997) 3291–3323
Math Reviews MR1465117
63
Minami, Norihiko
On the Hurewicz image of the cokernel J spectrum
Fund. Math. 155 (1998) 251–269
Math Reviews MR1607448
64
Fresse, Benoit
Iterated bar complexes of E-infinity algebras and homology theories.
arXiv:0810.5147
65
Fresse, Benoit
The bar complex of an E-infinity algebra.
math.AT/0601085
66
Stillwell, John
The word problem and the isomorphism problem for groups
Bull. Amer. Math. Soc. (N.S.) 6 (1982) 33–56
Math Reviews MR634433
67
Epstein, David B. A. and Cannon, James W. and Holt, Derek F. and Levy, Silvio V. F. and Paterson, Michael S. and Thurston, William P.
Word processing in groups
Jones and Bartlett Publishers, 1992
Math Reviews MR1161694
68
Bridson, Martin R.
The geometry of the word problem
in Invitations to geometry and topology
Oxf. Grad. Texts Math. 7 (2002) 29–91
Math Reviews MR1967746
69
Ching, Michael
A note on the composition product of symmetric sequences
math.CT/0510490
70
Cohen, Frederick R.
A course in some aspects of classical homotopy theory
in Algebraic topology (Seattle, Wash., 1985)
Lecture Notes in Math. 1286 (1987) 1–92
Math Reviews MR922923
71
Barratt, Michael and Priddy, Stewart
On the homology of non-connected monoids and their associated groups
Comment. Math. Helv. 47 (1972) 1–14
Math Reviews MR0314940
72
Priddy, Stewart B.
Transfer, symmetric groups, and stable homotopy theory
in Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972)
(1973) 244–255. Lecture Notes in Math. Vol. 341
Math Reviews MR0350727
73
Nakaoka, Minoru
Homology of the infinite symmetric group
Ann. of Math. 73 (1961) 229–257
Math Reviews MR0131874
74
Priddy, Stewart
Dyer-Lashof operations for the classifying spaces of certain matrix groups
Quart. J. Math. Oxford Ser. 26 (1975) 179–193
Math Reviews MR0375309
75
Kochman, Stanley O.
Homology of the classical groups over the Dyer-Lashof algebra
Trans. Amer. Math. Soc. 185 (1973) 83–136
Math Reviews MR0331386
76
Adem, Alejandro and Milgram, R. James
Cohomology of finite groups
Grund. Math. Wiss., vol. 309, Springer, 1994
Math Reviews MR1317096
77
Arone, Greg and Mahowald, Mark
The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres
Invent. Math. 135 (1999) 743–788
Math Reviews MR1669268
78
Hall, Marshall Jr.
The theory of groups
The Macmillan Co., 1959
Math Reviews MR0103215
79
Fox, Thomas F.
The construction of cofree coalgebras
J. Pure Appl. Algebra 84 (1993) 191–198
Math Reviews MR1201051
80
Ching, Michael
Bar constructions for topological operads and the Goodwillie derivatives of the identity
Geom. Topol. 9 (2005) 833–933
Math Reviews MR2140994
81
Walter, Ben
Cofree coalgebras over cooperads
In preparation
82
Sinha, Dev P. and Walter, Ben
Lie coalgebras and rational homotopy theory, II: Hopf invariants.
arXiv:0809.5084
83
Novikov, S. P.
Analytical theory of homotopy groups
in Topology and geometry—Rohlin Seminar
Lecture Notes in Math. 1346 (1988) 99–112
Math Reviews MR970074
84
Lambrechts, Pascal and Volic, Ismar
Formality of the little N-disks operad.
85
Haefliger, André
Whitehead products and differential forms
in Differential topology, foliations and Gelfand-Fuks cohomology (Proc. Sympos., Pontifícia Univ. Católica, Rio de Janeiro, 1976)
Lecture Notes in Math. 652 (1978) 13–24
Math Reviews MR505648
86
Kan, Daniel M.
A combinatorial definition of homotopy groups
Ann. of Math. 67 (1958) 282–312
Math Reviews MR0111032
87
Chen, Kuo-Tsai
Differential forms and homotopy groups
J. Differential Geometry 6 (1971/72) 231–246
Math Reviews MR0380858
88
Chen, Kuo Tsai
On Whitehead products
Proc. Amer. Math. Soc. 34 (1972) 257–259
Math Reviews MR0298659
89
Chen, Kuo Tsai
Iterated integrals, fundamental groups and covering spaces
Trans. Amer. Math. Soc. 206 (1975) 83–98
Math Reviews MR0377960
90
Tourtchine, Victor
On the other side of the bialgebra of chord diagrams
J. Knot Theory Ramifications 16 (2007) 575–629
Math Reviews MR2333307
91
Litherland, R. A.
Deforming twist-spun knots
Trans. Amer. Math. Soc. 250 (1979) 311–331
Math Reviews MR530058
92
André, Michel
Homologie des algèbres commutatives
Springer, 1974 Die Grundlehren der mathematischen Wissenschaften, Band 206
Math Reviews MR0352220
93
Quillen, Daniel
On the (co-) homology of commutative rings
in Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVII, New York, 1968)
(1970) 65–87
Math Reviews MR0257068
94
Budney, Ryan
A famly of embedding spaces
in Geometry and Topology Monographs
13 (2007)
95
Walter, Ben
Cooperads as symmetric sequences, I: Cofree coalgebras.
In preparation.
96
Feshbach, Mark
The mod 2 cohomology rings of the symmetric groups and invariants
Topology 41 (2002) 57–84
Math Reviews MR1871241
97
Bousfield, A. K. and Curtis, Edward B. and Kan, Daniel M. and Quillen, Daniel and Rector, D. L. and Schlesinger, J. W.
The mod-p lower central series and the Adams spectral sequence
Topology 5 (1966) 331–342
Math Reviews MR0199862
98
Barr, Michael
Harrison homology, Hochschild homology and triples
J. Algebra 8 (1968) 314–323
Math Reviews MR0220799
99
Fresse, Benoit
Koszul duality of operads and homology of partition posets
in Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic K-theory
Contemp. Math. 346 (2004) 115–215
Math Reviews MR2066499
100
Smith, Justin R.
Cofree coalgebras over operads
Topology Appl. 133 (2003) 105–138
Math Reviews MR1997960
101
Halperin, Stephen and Stasheff, James
Obstructions to homotopy equivalences
Adv. in Math. 32 (1979) 233–279
Math Reviews MR539532
102
J. Smith
Homotopy theory of coalgebras over operads
103
Ginzburg, Victor and Kaledin, Dmitry
Poisson deformations of symplectic quotient singularities
Adv. Math. 186 (2004) 1–57
Math Reviews MR2065506
104
Fresse, Benoit
Homologie de Quillen pour les algèbres de Poisson
C. R. Acad. Sci. Paris Sér. I Math. 326 (1998) 1053–1058
Math Reviews MR1647186
105
Harrison, D. K.
Commutative algebras and cohomology
Trans. Amer. Math. Soc. 104 (1962) 191–204
Math Reviews MR0142607
106
Voronov, Alexander A.
Homotopy Gerstenhaber algebras
in Conférence Moshé Flato 1999, Vol. II (Dijon)
Math. Phys. Stud. 22 (2000) 307–331
Math Reviews MR1805923
107
Voronov, Alexander A.
Homotopy Gerstenhaber algebras
108
Fox, R. and Neuwirth, Lee
The braid groups
Math. Scand. 10 (1962) 119–126
Math Reviews MR0150755
109
McClure, James E. and Smith, Jeffrey H.
Multivariable cochain operations and little n-cubes
J. Amer. Math. Soc. 16 (2003) 681–704
Math Reviews MR1969208
110
McClure, James E. and Smith, Jeffrey H.
A solution of Deligne's Hochschild cohomology conjecture
in Recent progress in homotopy theory (Baltimore, MD, 2000)
Contemp. Math. 293 (2002) 153–193
Math Reviews MR1890736
111
Berger, Clemens and Fresse, Benoit
Combinatorial operad actions on cochains
Math. Proc. Cambridge Philos. Soc. 137 (2004) 135–174
Math Reviews MR2075046
112
Sinha, Dev P.
The homology of the little disks operad
arXiv:math.AT/0610236
113
Adams, J. F.
On the non-existence of elements of Hopf invariant one
Ann. of Math. 72 (1960) 20–104
Math Reviews MR0141119
114
Sakai, Keiichi
Poisson structures on the homology of the space of knots
115
Salvatore, Paolo
Knots, operads and double loop spaces
116
Conant, James
Homotopy approximations to the space of knots, Feynman diagrams, and a conjecture of Scannell and Sinha
117
Adams, J. F. and Hilton, P. J.
On the chain algebra of a loop space
Comment. Math. Helv. 30 (1956) 305–330
Math Reviews MR0077929
118
Getzler, Ezra and Jones, J. D. S.
Operads, homotopy algebra and iterated integrals for double loop spaces
119
Longoni, Riccardo and Salvatore, Paolo
Configuration spaces are not homotopy invariant
Topology 44 (2005) 375–380
Math Reviews MR2114713
120
Boardman, J. M. and Steer, B.
On Hopf invariants
Comment. Math. Helv. 42 (1967) 180–221
Math Reviews MR0221503
121
Boardman, J. M. and Steer, B.
Axioms for Hopf invariants
Bull. Amer. Math. Soc. 72 (1966) 992–994
Math Reviews MR0202138
122
Whitehead, J. H. C.
An expression of Hopf's invariant as an integral
Proc. Nat. Acad. Sci. U. S. A. 33 (1947) 117–123
Math Reviews MR0020255
124
McClure, James E. and Smith, Jeffrey H.
Cosimplicial objects and little n-cubes. I
Amer. J. Math. 126 (2004) 1109–1153
Math Reviews MR2089084
125
Polyak, Michael and Viro, Oleg
On the Casson knot invariant
J. Knot Theory Ramifications 10 (2001) 711–738 Knots in Hellas '98, Vol. 3 (Delphi)
Math Reviews MR1839698
126
Lambrechts, Pascal and Tourtchine, Victor and Volic, Ismar
The homology of the space of long knots in codimension >2.
math.AT/0703649
127
Bousfield, A. K.
On the homology spectral sequence of a cosimplicial space
Amer. J. Math. 109 (1987) 361–394
Math Reviews MR882428
128
Kontsevich, Maxim
Operads of little disks in algebra and topology
(2000)
129
Koschorke, Ulrich
A generalization of Milnor's -invariants to higher-dimensional link maps
Topology 36 (1997) 301–324
Math Reviews MR1415590
130
Volic, Ismar
Finite-type knot invariants and the calculus of functors.
Compositio Math. 142 (2006) 222–250
131
Freedman, Michael H. and Krushkal, Vyacheslav S. and Teichner, Peter
van Kampen's embedding obstruction is incomplete for 2-complexes in <b>R</b>4
Math. Res. Lett. 1 (1994) 167–176
Math Reviews MR1266755
132
Weiss, Michael
Embeddings from the point of view of immersion theory. I
Geom. Topol. 3 (1999) 67–101
Math Reviews MR1694812
133
Goodwillie, Thomas G. and Klein, John R.
Excision estimates for spaces of embeddings.
In preparation.
134
Goodwillie, Thomas G. and Weiss, Michael
Embeddings from the point of view of immersion theory. II
Geom. Topol. 3 (1999) 103–118
Math Reviews MR1694808
135
Goodwillie, Thomas G. and Klein, John R. and Weiss, Michael S.
Spaces of smooth embeddings, disjunction and surgery
in Surveys on surgery theory, Vol. 2
Ann. of Math. Stud. 149 (2001) 221–284
Math Reviews MR1818775
136
Budney, Ryan
JSJ-decompositions of knot and link complements in the 3-sphere
137
Budney, Ryan
Topology of spaces of knots in dimension 3
138
Hatcher, Allen E.
A proof of a Smale conjecture, Diff(S3)O(4)
Ann. of Math. 117 (1983) 553–607
Math Reviews MR701256
139
Hatcher, Allen
Homeomorphisms of sufficiently large P2-irreducible 3-manifolds
Topology 15 (1976) 343–347
Math Reviews MR0420620
140
Hatcher, Allen
Spaces of Knots
(1999)
141
Kohno, Toshitake
Vassiliev invariants and de Rham complex on the space of knots
in Symplectic geometry and quantization (Sanda and Yokohama, 1993)
Contemp. Math. 179 (1994) 123–138
Math Reviews MR1319605
142
Bar-Natan, Dror and McKay, B.
Graph cohomology - an overview and some computations.
144
Chen, Kuo-tsai
Iterated integrals of differential forms and loop space homology
Ann. of Math. 97 (1973) 217–246
Math Reviews MR0380859
145
Chen, Kuo Tsai
Loop spaces and differential forms
in Algebraic homotopy and local algebra (Luminy, 1982)
Astérisque 113 (1984) 87–95
Math Reviews MR749044
146
Cattaneo, Alberto S. and Cotta-Ramusino, Paolo and Longoni, Riccardo
Configuration spaces and Vassiliev classes in any dimension
Algebr. Geom. Topol. 2 (2002) 949–1000
Math Reviews MR1936977
147
Kauffman, Louis H.
Vassiliev invariants and functional integration without integration
in Stochastic analysis and mathematical physics (SAMP/ANESTOC 2002)
(2004) 91–114
Math Reviews MR2115931
148
Thurston, Dylan P.
Integral Expressions for the Vassiliev Knot Invariants
149
Witten, Edward
Quantum field theory and the Jones polynomial
Comm. Math. Phys. 121 (1989) 351–399
Math Reviews MR990772
150
Witten, Edward
Quantum field theory and the Jones polynomial
in Braid group, knot theory and statistical mechanics, II
Adv. Ser. Math. Phys. 17 (1994) 361–451
Math Reviews MR1338609
151
Garoufalidis, Stavros and Teichner, Peter
On knots with trivial Alexander polynomial
J. Differential Geom. 67 (2004) 167–193
Math Reviews MR2153483
152
Vassiliev, Victor A.
Homology of spaces of knots in any dimensions
R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci. 359 (2001) 1343–1364 Topological methods in the physical sciences (London, 2000)
Math Reviews MR1853624
153
Vassiliev, Victor A.
Combinatorial formulas for cohomology of spaces of knots
in Advances in topological quantum field theory
NATO Sci. Ser. II Math. Phys. Chem. 179 (2004) 1–21
Math Reviews MR2147414
154
Vassiliev, Victor A.
On invariants and homology of spaces of knots in arbitrary manifolds
in Topics in quantum groups and finite-type invariants
Amer. Math. Soc. Transl. Ser. 2 185 (1998) 155–182
Math Reviews MR1736171
155
Vassiliev, Victor A.
Topology of two-connected graphs and homology of spaces of knots
in Differential and symplectic topology of knots and curves
Amer. Math. Soc. Transl. Ser. 2 190 (1999) 253–286
Math Reviews MR1738399
156
Vassiliev, Victor A.
Complements of discriminants of smooth maps: topology and applications
Translations of Mathematical Monographs, vol. 98, Amer. Math. Soc., 1992
Math Reviews MR1168473
157
Conant, James and Teichner, Peter
Grope cobordism of classical knots
Topology 43 (2004) 119–156
Math Reviews MR2030589
158
Stanford, Ted
Braid commutators and Vassiliev invariants
Pacific J. Math. 174 (1996) 269–276
Math Reviews MR1398378
159
Kuperberg, Greg and Thurston, Dylan P.
Perturbative 3-manifold invariants by cut-and-paste topology
160
Altschuler, Daniel and Freidel, Laurent
Vassiliev knot invariants and Chern-Simons perturbation theory to all orders
Comm. Math. Phys. 187 (1997) 261–287
Math Reviews MR1463829
161
Le, Tu Quoc Thang and Murakami, Jun
The universal Vassiliev-Kontsevich invariant for framed oriented links
Compositio Math. 102 (1996) 41–64
Math Reviews MR1394520
162
Bott, Raoul and Taubes, Clifford
On the self-linking of knots
J. Math. Phys. 35 (1994) 5247–5287 Topology and physics
Math Reviews MR1295465
163
Birman, Joan S.
New points of view in knot theory
Bull. Amer. Math. Soc. (N.S.) 28 (1993) 253–287
Math Reviews MR1191478
164
Birman, Joan S. and Lin, Xiao-Song
Knot polynomials and Vassiliev's invariants
Invent. Math. 111 (1993) 225–270
Math Reviews MR1198809
165
Calvo, Jorge Alberto
The embedding space of hexagonal knots
Topology Appl. 112 (2001) 137–174
Math Reviews MR1823601
166
E. Denne
PhD Thesis, University of Illinois (2004)
167
Kuperberg, Greg
Quadrisecants of knots and links
J. Knot Theory Ramifications 3 (1994) 41–50
Math Reviews MR1265452
168
Morton, H. R. and Mond, D. M. Q.
Closed curves with no quadrisecants
Topology 21 (1982) 235–243
Math Reviews MR649756
169
Kontsevich, Maxim
Vassiliev's knot invariants
in I. M. Gelfand Seminar
Adv. Soviet Math. 16 (1993) 137–150
Math Reviews MR1237836
170
Habiro, Kazuo
Claspers and finite type invariants of links
Geom. Topol. 4 (2000) 1–83
Math Reviews MR1735632
171
Goussarov, Mikhail and Polyak, Michael and Viro, Oleg
Finite-type invariants of classical and virtual knots
Topology 39 (2000) 1045–1068
Math Reviews MR1763963
172
Bar-Natan, Dror and Stoimenow, Alexander
The fundamental theorem of Vassiliev invariants
in Geometry and physics (Aarhus, 1995)
Lecture Notes in Pure and Appl. Math. 184 (1997) 101–134
Math Reviews MR1423158
173
Bar-Natan, Dror
On the Vassiliev knot invariants
Topology 34 (1995) 423–472
Math Reviews MR1318886
174
Goussarov, Mikhail
On n-equivalence of knots and invariants of finite degree
in Topology of manifolds and varieties
Adv. Soviet. Math., vol. 18 (1994) 173–192
175
Sinha, Dev P.
The topology of spaces of knots: cosimplicial models
Amer. J. Math. (2009)
176
Scannell, Kevin P. and Sinha, Dev P.
A one-dimensional embedding complex
J. Pure Appl. Algebra 170 (2002) 93–107
Math Reviews MR1896343
177
Budney, Ryan
Little cubes and long knots
Topology 46 (2007) 1–27
178
Tourtchine, Victor
On the homology of the spaces of long knots
in Advances in topological quantum field theory
NATO Sci. Ser. II Math. Phys. Chem. 179 (2004) 23–52
Math Reviews MR2147415
179
Sinha, Dev
Bordism of semi-free S1-actions
Math. Z. 249 (2005) 439–454
Math Reviews MR2115453
180
Sinha, Dev P.
Operads and knot spaces
J. Amer. Math. Soc. 19 (2006) 461–486
Math Reviews MR2188133
181
Sinha, Dev P. and Walter, Ben
Lie coalgebras and rational homotopy theory, I: graph coalgebras.
math.AT/0610437
182
May, J. Peter
Homology operations on infinite loop spaces
in Algebraic topology (Proc. Sympos. Pure Math., Vol. XXII, Univ. Wisconsin, Madison, Wis., 1970)
(1971) 171–185
Math Reviews MR0319195
183
Dyer, Eldon and Lashof, R. K.
Homology of iterated loop spaces
Amer. J. Math. 84 (1962) 35–88
Math Reviews MR0141112
184
Boardman, J. M. and Vogt, R. M.
Homotopy invariant algebraic structures on topological spaces
Springer, 1973 Lecture Notes in Mathematics, Vol. 347
Math Reviews MR0420609
185
Axelrod, Scott and Singer, I. M.
Chern-Simons perturbation theory. II
J. Differential Geom. 39 (1994) 173–213
Math Reviews MR1258919
186
Fulton, William and MacPherson, Robert
A compactification of configuration spaces
Ann. of Math. 139 (1994) 183–225
Math Reviews MR1259368
187
Fadell, Edward R. and Husseini, Sufian Y.
Geometry and topology of configuration spaces
Springer Monographs in Math., Springer, 2001
Math Reviews MR1802644
188
Sinha, Dev P.
Manifold-theoretic compactifications of configuration spaces
Selecta Math. (N.S.) 10 (2004) 391–428
Math Reviews MR2099074
189
May, J. Peter
The geometry of iterated loop spaces
Springer, 1972
Math Reviews MR0420610
190
McClure, James E. and Smith, Jeffrey H.
Operads and cosimplicial objects: an introduction
in Axiomatic, enriched and motivic homotopy theory
NATO Sci. Ser. II Math. Phys. Chem. 131 (2004) 133–171
Math Reviews MR2061854
191
Milnor, John W. and Moore, John C.
On the structure of Hopf algebras
Ann. of Math. 81 (1965) 211–264
Math Reviews MR0174052
192
Cohen, Frederick R.
On configuration spaces, their homology, and Lie algebras
J. Pure Appl. Algebra 100 (1995) 19–42
Math Reviews MR1344842
193
Cohen, Frederick R.
Cohomology of braid spaces
Bull. Amer. Math. Soc. 79 (1973) 763–766
Math Reviews MR0321074
194
Cohen, Frederick R. and Lada, Thomas J. and May, J. Peter
The homology of iterated loop spaces
Springer, 1976
Math Reviews MR0436146
195
Ginzburg, Victor and Kapranov, Mikhail
Koszul duality for operads
Duke Math. J. 76 (1994) 203–272
Math Reviews MR1301191
196
Baues, H. J. and Lemaire, J.-M.
Minimal models in homotopy theory
Math. Ann. 225 (1977) 219–242
Math Reviews MR0431172
197
Schwede, Stefan and Shipley, Brooke E.
Algebras and modules in monoidal model categories
Proc. London Math. Soc. 80 (2000) 491–511
198
Aubry, Marc and Chataur, David
Cooperads and coalgebras as closed model categories
J. Pure Appl. Algebra 180 (2003) 1–23
Math Reviews MR1966520
199
Hirschhorn, Philip S.
Model categories and their localizations
Mathematical Surveys and Monographs, vol. 99, Amer. Math. Soc., 2003
Math Reviews MR1944041
200
Walter, Ben
Rational homotopy theory from the operadic point of view.
In preparation.
201
Sinha, Dev P. and Walter, Ben
Lie coalgebras and rational homotopy theory, II. Hopf invariants.
In preparation.
202
Sullivan, Dennis
Infinitesimal computations in topology
Publ. Math. I.H.É.S. 47 (1977) 269–331 (1978)
Math Reviews MR0646078
203
Quillen, Daniel
Rational homotopy theory
Ann. of Math. 90 (1969) 205–295
Math Reviews MR0258031
204
Sinha, Dev P.
A pairing between graphs and trees.
(2006) math.QA/0502547
205
Sinha, Dev P.
Operads and knot spaces
J. Amer. Math. Soc. 19 (2006) 461–486
Math Reviews MR2188133
206
Michaelis, Walter
Lie coalgebras
Adv. in Math. 38 (1980) 1–54
Math Reviews MR594993
207
Félix, Yves and Halperin, Stephen and Thomas, Jean-Claude
Rational homotopy theory
Graduate Texts in Math., vol. 205, Springer, 2001
Math Reviews MR1802847
208
Melançon, Guy and Reutenauer, Christophe
Free Lie superalgebras, trees and chains of partitions
J. Algebraic Combin. 5 (1996) 337–351
Math Reviews MR1406458
209
Markl, Martin and Shnider, Steve and Stasheff, Jim
Operads in algebra, topology and physics
Mathematical Surveys and Monographs, vol. 96, Amer. Math. Soc., 2002
Math Reviews MR1898414
210
Arnold, V. I.
The cohomology ring of the group of dyed braids
Mat. Zametki 5 (1969) 227–231
Math Reviews MR0242196
211
Kontsevich, Maxim and Soibelman, Yan
Deformations of algebras over operads and the Deligne conjecture
in Conférence Moshé Flato 1999, Vol. I (Dijon)
Math. Phys. Stud. 21 (2000) 255–307
Math Reviews MR1805894
212
Hain, Richard M.
Iterated integrals and homotopy periods
Mem. Amer. Math. Soc. 47 (1984) 98
Math Reviews MR727818
213
Sinha, Dev P.
Bordism of semi-free S1-actions
Math. Z. 249 (2005) 439–454
Math Reviews MR2115453
214
Budney, Ryan and Conant, James and Scannell, Kevin P. and Sinha, Dev
New perspectives on self-linking
Adv. Math. 191 (2005) 78–113
Math Reviews MR2102844