Geometry & Topology Volume 14, issue 4 (2010)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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The rational homology of spaces of long knots in codimension $\gt 2$

Pascal Lambrechts, Victor Turchin and Ismar Volić

Geometry & Topology 14 (2010) 2151–2187

DOI: 10.2140/gt.2010.14.2151

Bibliography

1	G Arone, P Lambrechts, V Turchin, I Volić, Coformality and rational homotopy groups of spaces of long knots, Math. Res. Lett. 15 (2008) 1 MR2367169
2	G Arone, P Lambrechts, I Volić, Calculus of functors, operad formality, and rational homology of embedding spaces, Acta Math. 199 (2007) 153 MR2358051
3	S Axelrod, I M Singer, Chern–Simons perturbation theory. II, J. Differential Geom. 39 (1994) 173 MR1258919
4	R Bott, C Taubes, On the self-linking of knots. Topology and physics, J. Math. Phys. 35 (1994) 5247 MR1295465
5	A K Bousfield, On the homology spectral sequence of a cosimplicial space, Amer. J. Math. 109 (1987) 361 MR882428
6	A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR0365573
7	A S Cattaneo, P Cotta-Ramusino, R Longoni, Configuration spaces and Vassiliev classes in any dimension, Algebr. Geom. Topol. 2 (2002) 949 MR1936977
8	F R Cohen, T J Lada, J P May, The homology of iterated loop spaces, 533, Springer (1976) MR0436146
9	P Deligne, P Griffiths, J Morgan, D Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math. 29 (1975) 245 MR0382702
10	Y Félix, S Halperin, J C Thomas, Rational homotopy theory, 205, Springer (2001) MR1802847
11	G Gaiffi, Models for real subspace arrangements and stratified manifolds, Int. Math. Res. Not. (2003) 627 MR1951400
12	M Gerstenhaber, A A Voronov, Homotopy G–algebras and moduli space operad, Internat. Math. Res. Notices (1995) 141 MR1321701
13	E Getzler, J D S Jones, Operads, homotopy algebra and iterated integrals for double loop spaces arXiv:hep-th/9403055
14	P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser Verlag (1999) MR1711612
15	T G Goodwillie, J R Klein, M S Weiss, Spaces of smooth embeddings, disjunction and surgery, from: "Surveys on surgery theory, Vol. 2" (editors S Cappell, A Ranicki, J Rosenberg), Ann. of Math. Stud. 149, Princeton Univ. Press (2001) 221 MR1818775
16	M Kontsevich, Vassiliev’s knot invariants, from: "I M Gel’fand Seminar" (editors S Gel’fand, S Gindikin), Adv. Soviet Math. 16, Amer. Math. Soc. (1993) 137 MR1237836
17	M Kontsevich, Feynman diagrams and low-dimensional topology, from: "First European Congress of Mathematics, Vol. II (Paris, 1992)", Progr. Math. 120, Birkhäuser (1994) 97 MR1341841
18	M Kontsevich, Operads and motives in deformation quantization, Lett. Math. Phys. 48 (1999) 35 MR1718044
19	M Kontsevich, Y Soibelman, Deformations of algebras over operads and the Deligne conjecture, from: "Conférence Moshé Flato 1999, Vol. I (Dijon)" (editors G Dito, D Sternheimer), Math. Phys. Stud. 21, Kluwer Acad. Publ. (2000) 255 MR1805894
20	P Lambrechts, V Turchin, Homotopy graph-complex for configuration and knot spaces, Trans. Amer. Math. Soc. 361 (2009) 207 MR2439404
21	P Lambrechts, V Turchin, I Volić, Associahedron, cyclohedron and permutohedron as compactifications of configuration spaces, Bull. Belg. Math. Soc. Simon Stevin 17 (2010) 303 MR2663475
22	P Lambrechts, I Volić, Formality of the little N–discs operad, Preprint (2010)
23	M Markl, A compactification of the real configuration space as an operadic completion, J. Algebra 215 (1999) 185 MR1684178
24	M Markl, S Shnider, J Stasheff, Operads in algebra, topology and physics, 96, Amer. Math. Soc. (2002) MR1898414
25	J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR0420610
26	J E McClure, J H Smith, A solution of Deligne’s Hochschild cohomology conjecture, from: "Recent progress in homotopy theory (Baltimore, MD, 2000)" (editors D M Davis, J Morava, G Nishida, W S Wilson, N Yagita), Contemp. Math. 293, Amer. Math. Soc. (2002) 153 MR1890736
27	P Salvatore, Configuration operads, minimal models and rational curves, PhD thesis, Oxford University (1998)
28	K P Scannell, D P Sinha, A one-dimensional embedding complex, J. Pure Appl. Algebra 170 (2002) 93 MR1896343
29	D P Sinha, Manifold-theoretic compactifications of configuration spaces, Selecta Math. (N.S.) 10 (2004) 391 MR2099074
30	D P Sinha, Operads and knot spaces, J. Amer. Math. Soc. 19 (2006) 461 MR2188133
31	D P Sinha, The topology of spaces of knots: cosimplicial models, Amer. J. Math. 131 (2009) 945 MR2543919
32	S Smale, The classification of immersions of spheres in Euclidean spaces, Ann. of Math. (2) 69 (1959) 327 MR0105117
33	V Tourtchine (Turchin), On the homology of the spaces of long knots, from: "Advances in topological quantum field theory" (editor J M Bryden), NATO Sci. Ser. II Math. Phys. Chem. 179, Kluwer Acad. Publ. (2004) 23 MR2147415
34	V Tourtchine (Turchin), What is one-term relation for higher homology of long knots, Mosc. Math. J. 6 (2006) 169, 223 MR2265954
35	V Tourtchine (Turchin), On the other side of the bialgebra of chord diagrams, J. Knot Theory Ramifications 16 (2007) 575 MR2333307
36	V A Vassiliev, Cohomology of knot spaces, from: "Theory of singularities and its applications" (editor V I Arnol’d), Adv. Soviet Math. 1, Amer. Math. Soc. (1990) 23 MR1089670
37	V A Vassiliev, Invariants of knots and complements of discriminants, from: "Developments in mathematics : the Moscow school" (editors V I Arnol’d, M Monastyrsky), Chapman & Hall (1993) 194 MR1264426
38	V A Vassiliev, Homology of i–connected graphs and invariants of knots, plane arrangements, etc, from: "The Arnoldfest (Toronto, ON, 1997)" (editors E Bierstone, B Khesin, A Khovanskii, J E Marsden), Fields Inst. Commun. 24, Amer. Math. Soc. (1999) 451 MR1733588
39	C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324