Geometry & Topology Volume 13, issue 1 (2009)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

On the homology of the space of knots

Ryan Budney and Fred Cohen

Geometry & Topology 13 (2009) 99–139

DOI: 10.2140/gt.2009.13.99

Bibliography

1	D Altschüler, L Freidel, On universal Vassiliev invariants, Comm. Math. Phys. 170 (1995) 41 MR1331690
2	D Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995) 423 MR1318886
3	F Bonahon, L Siebenmann, Geometric splittings of knots and Conway's algebraic knots, unpublished preprint (1987)
4	R Bott, C Taubes, On the self-linking of knots, J. Math. Phys. 35 (1994) 5247 MR1295465
5	R Budney, The topology of knotspaces in dimension $3$ arXiv:math/0506524
6	R Budney, JSJ–decompositions of knot and link complements in $S^3$, Enseign. Math. $(2)$ 52 (2006) 319 MR2300613
7	R Budney, Little cubes and long knots, Topology 46 (2007) 1 MR2288724
8	R Budney, A family of embedding spaces, from: "Groups, homotopy and configuration spaces (Tokyo 2005)" (editors N Iwase, T Kohno, R Levi, D Tamaki, J Wu), Geometry and Topology Monographs 13 (2008) 41
9	R Budney, J Conant, K P Scannell, D Sinha, New perspectives on self-linking, Adv. Math. 191 (2005) 78 MR2102844
10	A S Cattaneo, P Cotta-Ramusino, R Longoni, Configuration spaces and Vassiliev classes in any dimension, Algebr. Geom. Topol. 2 (2002) 949 MR1936977
11	V Chari, A Pressley, A guide to quantum groups, Cambridge University Press (1994) MR1300632
12	F R Cohen, T J Lada, J P May, The homology of iterated loop spaces, Lecture Notes in Mathematics, Vol. 533, Springer (1976) MR0436146
13	D Eisenbud, W Neumann, Three-dimensional link theory and invariants of plane curve singularities, Annals of Mathematics Studies, Princeton University Press (1985) MR817982
14	T G Goodwillie, M Weiss, Embeddings from the point of view of immersion theory. II, Geom. Topol. 3 (1999) 103 MR1694808
15	A Gramain, Sur le groupe fundamental de l'espace des noeuds, Ann. Inst. Fourier (Grenoble) 27 (1977) 29 MR0461567
16	A Haefliger, Differential embeddings of $S^{n}$ in $S^{n+q}$ for $q \gt 2$, Ann. of Math. $(2)$ 83 (1966) 402 MR0202151
17	A Hatcher, Spaces of Knots arXiv:math.GT/9909095
18	A Hatcher, Homeomorphisms of sufficiently large $P^{2}$–irreducible $3$–manifolds, Topology 15 (1976) 343 MR0420620
19	A Hatcher, Topological Moduli Spaces of Knots (2002)
20	N Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons), New York-London (1962) MR0143793
21	T Kanenobu, Hyperbolic links with Brunnian properties, J. Math. Soc. Japan 38 (1986) 295 MR833204
22	A Kawauchi, A survey of knot theory, Birkhäuser Verlag (1996) MR1417494
23	T Kohno, Vassiliev invariants and de Rham complex on the space of knots, from: "Symplectic geometry and quantization (Sanda and Yokohama, 1993)", Contemp. Math. 179, Amer. Math. Soc. (1994) 123 MR1319605
24	T Kohno, Loop spaces of configuration spaces and finite type invariants, from: "Invariants of knots and 3-manifolds (Kyoto, 2001)" (editors T Ohtsuki, e al), Geom. Topol. Monogr. 4 (2002) 143 MR2002608
25	M Kontsevich, Feynman diagrams and low-dimensional topology, from: "First European Congress of Mathematics, Vol. II (Paris, 1992)", Progr. Math., Birkhäuser (1994) 97 MR1341841
26	P Lambrechts, V Turchin, I Volic, The rational homotopy type of spaces of knots in codimension $\gt 2$, preprint
27	C Lescop, On configuration space integrals for links, from: "Invariants of knots and 3–manifolds (Kyoto, 2001)" (editors T Ohtsuki, e al), Geom. Topol. Monogr. 4 (2002) 183 MR2002610
28	S Manfredini, Some subgroups of Artin's braid group, Topology Appl. 78 (1997) 123 MR1465028
29	J P May, The geometry of iterated loop spaces, Lectures Notes in Mathematics 271, Springer (1972) MR0420610
30	J W Milnor, J C Moore, On the structure of Hopf algebras, Ann. of Math. $(2)$ 81 (1965) 211 MR0174052
31	R S Palais, Local triviality of the restriction map for embeddings, Comment. Math. Helv. 34 (1960) 305 MR0123338
32	M Polyak, O Viro, On the Casson knot invariant, J. Knot Theory Ramifications 10 (2001) 711 MR1839698
33	K Sakai, Non-trivalent graph cocycle and cohomology of the long knot space, Algebr. Geom. Topol. 8 (2008) 1499
34	P Salvatore, Knots, operads, and double loop spaces, Int. Math. Res. Not. (2006) 22 MR2276349
35	H Schubert, Die eindeutige Zerlegbarkeit eines Knotens in Primknoten, S-B Heidelberger Akad. Wiss. Math.-Nat. Kl. 1949 (1949) 57 MR0031733
36	H Schubert, Knoten und Vollringe, Acta Math. 90 (1953) 131 MR0072482
37	D Sinha, The topology of spaces of knots arXiv:math.AT/0202287
38	W P Thurston, Three-dimensional geometry and topology. Vol. 1, Princeton Mathematical Series 35, Princeton University Press (1997) MR1435975
39	V Tourtchine, On the other side of the bialgebra of chord diagrams, J. Knot Theory Ramifications 16 (2007) 575 MR2333307
40	V A Vassiliev, Complements of discriminants of smooth maps: topology and applications, Translations of Mathematical Monographs 98, American Mathematical Society (1992) MR1168473
41	I Volić, Finite type knot invariants and the calculus of functors, Compos. Math. 142 (2006) 222 MR2197410
42	T Watanabe, Configuration space integral for long $n$-knots and the Alexander polynomial, Algebr. Geom. Topol. 7 (2007) 47 MR2289804
43	H Whitney, Differentiable manifolds, Ann. of Math. $(2)$ 37 (1936) 645 MR1503303
44	W Wu, On the isotopy of $C^{r}$–manifolds of dimension $n$ in euclidean $(2n+1)$–space, Sci. Record $($N.S.$)$ 2 (1958) 271 MR0104272