On finite type 3-manifold invariants I

Journal of Knot Theory and its Ramifications

Volumn 5, Issue 4, 1996, Pages 441-461

  Garoufalidis, Stavros ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030491822     PISSN: 02182165     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218216596000278     Document Type: Article

References (35)

1. S. Akbulut, J. C. McCarthy, Casson's invariant for oriented homology 3-spheres: an exposition, Princeton Math Notes, Princeton, 1990.
2. M. F. Atiyah, Topological Quantum Field Theories, I.H.E.S. Publ. Math. 68 (1988) 175-186.
3. S. Axelrod, I. M. Singer, Chern-Simons pertrubation theory, Proc. XXth DGM Conference (New York, 1991) World Scientific, (1992) 3-45.
4. S. Axelrod, I. M. Singer, Perturbative aspects of Chern-Simons topological quantum field theory II, Jour. Diff. Geom. 39 (1994) 173-213.
5. D. Bar-Natan, On the Vassiliev knot invariants, preprint 1992, (to appear in Topology).
6. _, Computer data files available via anonymous file transfer from math. harvard. edu, user name ftp, subdirectory dror. Read the file README first.
7. D. Bar-Natan, S. Garoufalidis, On the Melvin-Morton-Hozansky conjecture, preprint 1994, submitted to Inventiones.
8. J. Birman, X-S. Lin, Knot polynomials and Vassiliev's invariants, Invent. Math. 111 (1993) 225-270.
9. R. Bott, C. Taubes, On the self linking of knots, preprint 1994.
10. V. G. Drinfeld, On quasitriangular quasi Hopf algebras and a group closely connected with Gal(ℚ̄/ℚ), Leningrad Math. J. 2 (1991) 829-860.
11. B. Ewing, K. Millett, poly.c, available at millett@math.ucsb.edu.
12. S. Garoufalidis, J. Levine, On finite type 3-manifold invariants II, Brandeis Univ. and M.I.T. preprint June 1995, to appear in Math. Annalen.
13. _, On finite type 3-manifold invariants IV: comparison of definitions, Brandeis Univ. and M.I.T. preprint September 1995, to appear in Proc. Camb. Phil. Soc.
14. S. Garoufalidis, T. Ohtsuki, On finite type 3-manifold invariants III: manifold weight systems, Tokyo Institute of Technology and M.I.T. preprint August 1995.
15. _, On finite type 3-manifold invariants V: rational homology 3-spheres , Tokyo Institute of Technology and M.I.T. preprint August 1995, to appear in Proceedings of the Aarhus conference.
16. N. Habegger, Finite type 3-manifold invariants: a proof of a conjecture of Garoufalidis, preprint, July 1995.
17. C. Kassel, Quantum groups, to appear in GTM, Springer-Verlag, Heidelberg 1994.
18. L. Kauffman, Invariants of 3-manifolds derived from finite dimensional Hopf algebras, hep-th preprint 9406065.
19. R. Kirby, P. Melvin, The 3-manifold invariants of Reshetikhin-Turaev for sl(2, ℂ), Inventiones, 105 (1991) 473-545.
20. T. Kohno, Topological invariants of 3-manifolds using representations of mapping class groups I, Topology, 31 (1992) 203-230.
21. M. Kontsevich, Vassiliev's knot invariants, Adv. in Sov. Math., 16(2) (1993), 137-150.
22. _, Graphs, homotopical algebra and low dimensional topology, preprint 1992.
23. G. Kuperberg, Non-involutory Hopf algebras and 3-manifold invariants, preprint 1994.
24. T.Q.T. Le, J. Murakami, The universal Vassiliev-Kontsevich invariant for framed oriented links, Max-Plank-Institut Bonn preprint, 1993.
25. W.B.R. Lickorish, Surgery on knots, Proc. Amer. Math. Society, 60 (1976) 296-298.
26. M. Ochiai, Knot theory by computer, available at ochai@ics.nara-wu.ac.jp.
27. T. Ohtsuki, A polynomial invariant of integral homology spheres, Math. Proc. Camb. Phil. Soc. 117 (1995) 83-112.
28. _, Finite type invariants of integral homology 3-spheres, preprint 1994, to appear in J. Knot Theory and its Rami.
29. M. Polyak, A graphical approach to the 3-manifold invariants of Turaev and Viro, J. Knot Theory 1 (1992) 219-240.
30. N. Reshetikhin, V. Turaev, Ribbon graphs and their invariants derived from quantum groups, Commun. Math. Phys. 127 (1990) 1-26.
31. _, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991) 547-597.
32. D. Rolfsen, Knots and links, Publish or Perish, 1976.
33. V. Turaev, H. Wenzl, Quantum invariants of 3-manifolds associated with classical simple Lie algebras, Inter. J. Math. 4 (1993) 323-358.
34. V. A. Vassiliev, Complements of discriminants of smooth maps, Trans. of Math. Mono. 98 Amer. Math. Society., Providence, 1992.
35. E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121 (1989) 360-376.