Volume 13, issue 1 (2009)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24, 1 issue

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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
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3 F Bonahon, L Siebenmann, Geometric splittings of knots and Conway's algebraic knots, unpublished preprint (1987)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