Claspers and finite type invariants of links

Geometry and Topology

Volumn 4, Issue , 2000, Pages 1-83

  Habiro, Kazuo ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Clasper; Link; String link; Vassiliev goussarov invariant

Indexed keywords

EID: 0003157001     PISSN: 14653060     EISSN: None     Source Type: Journal    
DOI: 10.2140/gt.2000.4.1     Document Type: Article

References (46)

1. D Bar-Natan, On the Vassiliev knot invariants, Topology, 34 (1995) 423-472
2. D Bar-Natan, Vassiliev homotopy string link invariants, J. Knot Theory Ramifications, 4 (1995) 13-32
3. JS Birman, New points of view in knot theory, Bull. Amer. Math. Soc. 28 (1993) 253-287
4. JS Birman, XS Lin, Knot polynomials and Vassiliev's invariants, Invent. Math. 111 (1993) 225-270
5. TD Cochran, Derivatives of links: Milnor's concordance invariants and Massey's products, Mem. Amer. Math. Soc. 84 (1990) no. 427
6. TD Cochran, A Gerges, K Orr, Surgery equivalence relations on three- manifolds, preprint
7. TD Cochran, PM Melvin, Finite type invariants of 3-manifolds, preprint
8. L Crane, D Yetter, On algebraic structures implicit in Topological Quantum Field Theories, preprint
9. MH Freedman, P Teichner, 4-Manifold topology II: Dwyer's filtration and surgery kernels, Invent. Math. 122 (1995) 531-557
10. S Garoufalidis, N Habegger, The Alexander polynomial and finite type 3-manifold invariants, preprint
11. S Garoufalidis, J Levine, Finite type 3-manifold invariants, the mapping class group and blinks, J. Diff. Geom. 47 (1997) 257-320
12. S Garoufalidis,T Ohtsuki, On finite type 3-manifold invariants III: manifold weight systems, Topology, 37 (1998) 227-243
13. MN Goussarov, A new form of the Conway-Jones polynomial of oriented links, from: "Topology of manifolds and varieties", Adv. Soviet Math. 18, Amer. Math. Soc. Providence, RI (1994) 167-172
14. MN Goussarov, On n-equivalence of knots and invariants of finite degree, from: "Topology of manifolds and varieties", Adv. Soviet Math. 18, Amer. Math. Soc. Providence, RI (1994) 173-192
15. MN Goussarov, Interdependent modifications of links and invariants of finite degree, Topology, 37 (1998) 595-602
16. MN Goussarov, New theory of invariants of finite degree for 3-manifolds, (in Russian) preprint
17. N Habegger, A computation of the universal quantum 3-manifold invariant for manifolds of rank greater than 2, preprint
18. N Habegger, XS Lin, The classification of links up to link-homotopy, J.Amer. Math. Soc. 3 (1990) 389-419
19. N Habegger, G Masbaum, The Kontsevich integral and Milnor's invariants, preprint
20. K Habiro, Claspers and the Vassiliev skein modules, PhD thesis, University of Tokyo (1997)
21. K Habiro, Clasp-pass moves on knots, unpublished
22. R Hain, Infinitesimal presentations of the Torelli groups, J. Amer. Math. Soc. 10 (1997) 597-651
23. D Johnson, An abelian quotient of the mapping class group, Math. Ann. 249 (1980) 225-242
24. T Kerler, Genealogy of nonperturbative quantum-invariants of 3-manifolds: The surgical family, from: "Geometry and physics", Lecture Notes in Pure and Appl. Math. 184, Dekker, New York (1997) 503-547
25. T Kerler, Bridged links and tangle presentations of cobordism categories, preprint
26. 3, Invent. Math. 65 (1978) 35-56
27. T Kohno, Vassiliev invariants and de-Rham complex on the space of knots, from: "Symplectic geometry and quantization", Contemp. Math. 179, Amer. Math. Soc. Providence, RI (1994) 123-138
28. M Kontsevich, Vassiliev's knot invariants, from: "IM Gelfand seminar", Adv. Soviet Math. 16 Part 2, Amer. Math. Soc. Providence, RI (1993) 137-150
29. VS Krushkal, Additivity properties of Milnor's μ̄-invariants, J. Knot Theory Ramifications, 7 (1998) 625-637
30. TQT Le, An invariant of integral homology 3-spheres which is universal for all finite type invariants, from: "Solitons, geometry and topology: on the crossroad", Amer. Math. Soc. Transl. Ser. 2, 179 (1997) 75-100,
31. TQT Le, J Murakami, T Ohtsuki, On a universal quantum invariant of 3-manifolds, Topology, 37 (1998) 539-574
32. XS Lin, Power series expansions and invariants of links, from "Geometric topology", AMS/IP Stud. Adv. Math. 2.1, Amer. Math. Soc. Providence, RI (1997) 184-202
33. S Majid, Algebras and Hopf algebras in braided categories, from: "Advances in Hopf algebras", Lecture Notes in Pure and Appl. Math. 158, Dekker, New York (1994) 55-105
34. S Majid, Foundations of quantum group theory, Cambridge University Press, Cambridge (1995)
35. SV Matveev, Generalized surgeries of three-dimensional manifolds and representations of homology spheres, (in Russian) Mat. Zametki 42 (1987) 268-278, 345
36. J Milnor, Link groups, Ann. of Math. 59 (1954) 177-195
37. J Milnor, Isotopy of links Algebraic geometry and topology, from: "A symposium in honor of S Lefschetz", Princeton University Press, Princeton, NJ (1957) 280-306
38. S Morita, Casson's invariant for homology 3-spheres and characteristic classes of surface bundles I, Topology, 28 (1989) 305-323
39. SMorita, Abelian quotients of subgroups of the mapping class group of surfaces, Duke Math. J. 70 (1993) 699-726
40. H Murakami, Y Nakanishi, On a certain move generating link-homology, Math. Ann. 284 (1989) 75-89
41. KY Ng, Groups of ribbon knots, Topology, 37 (1998) 441-458
42. T Ohtsuki, Finite type invariants of integral homology 3-spheres, J. Knot Theory Ramifications, 5 (1996) 101-115
43. T Stanford, Finite type invariants of knots, links, and graphs, Topology, 35 (1996) 1027-1050
44. T Stanford, Braid commutators and Vassiliev invariants, Pacific Jour. of Math. 174 (1996) 269-276
45. T Stanford, Vassiliev invariants and knots modulo pure braid subgroups, preprint
46. VA Vassiliev, Cohomology of knot spaces, from: "Theory of Singularities and its Applications", Adv. Soviet Math., Amer. Math. Soc. Providence, RI (1990) 23-69