On p-adic convergence of perturbative invariants of some rational homology spheress

Duke Mathematical Journal

Volumn 91, Issue 2, 1998, Pages 353-379

  Rozansky, L ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0009045028     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-98-09115-3     Document Type: Article

References (29)

1. S. Akbulut and D. J. McCarthy, Cassoris Invariant for Oriented Homology 3-Spheres: An Exposition, Math. Notes 36, Princeton Univ. Press, Princeton, 1990.
2. D. Bar-Natan, Perturbative Chern-Simons theory, J. Knot Theory Ramifications 4 (1995), 503-547.
3. D. Bar-Natan and S. Garoufalidis, On the Melvin-Morton-Rozansky conjecture, Invent. Math. 125 (1996), 103-133.
4. G. Burde and H. Zieschang, Knots, de Gruyter Stud. Math. 5, de Gruyter, Berlin, 1985.
5. D. Freed and R. Gompf, Computer calculation of Witten’s 3-manifold invariant, Comm. Math. Phys. 141 (1991), 79-117.
6. L. Jeffrey, Chern-Simons-Witten invariants of lens spaces and torus bundlesand the semi-classical approximation, Comm. Math. Phys. 147 (1992), 563-604.
7. R. Kirby and P. Melvin, The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2,0, Invent. Math. 105 (1991), 473-545.
8. M. Kontsevich, “V assiliev’s knot invariants” in I. M. Gelfand Seminar, Adv. Sov. Math. 16, Amer. Math. Soc., Providence, 1993,137-150.
9. R. Lawrence, Asymptotic expansions of Witten-Reshetikhin-Turaev invariants for some simple 3-manifolds, J. Math. Phys. 36 (1995), 6106-6129.
10. C. Lescop, Invariant de Casson-Walker des sphères d’homologie rationnelle fibrées de Seifert, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), 727-730.
11. X. S. Lin and Z. Wang, On OhtsukVs invariants of integral homology spheres, I, preprint, q-alg/ 9509009.
12. G. Masbaum and J. Roberts, A simple proof of integrality of quantum invariants at prime roots of unity, Math. Proc. Cambridge Philos. Soc. 121 (1997), 443-454.
13. P. Melvin and H. Morton, The coloured Jones function, Comm. Math. Phys. 169 (1995), 501-520.
14. H. Murakami, Quantum SU(2)-invariants dominate Casson’s SU(2)-invariant, Math. Proc. Cambridge Philos. Soc. 115 (1994), 253-281.
15. H. Murakami, Quantum SO(3)-invariants dominate the SU(2)-invariant of Casson and Walker, Math. Proc. Cambridge Philos. Soc. 117 (1995), 237-249.
16. T. Ohtsuki, A polynomial invariant of integral homology 3-spheres, Math. Proc. Cambridge Philos. Soc. 117 (1995), 83-112.
17. T. Ohtsuki, A polynomial invariant of rational homology 3-spheres, Invent Math. 123 (1996), 241-257.
18. N. Reshetikhin and V. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent Math. 103 (1991), 547-597.
19. L. Rozansky, A large k asymptotics of Witten’s invariant of Seifert manifolds, Comm. Math. Phys. 171 (1995), 279-322.
20. L. Rozansky, Reshetikhin’s formula for the Jones polynomial of a link: Feynman diagrams and Milnor’s linking numbers, J. Math. Phys. 35 (1994), 5219-5246.
21. L. Rozansky, A contribution of the trivial connection to the Jones polynomial and Witten’s invariant of 3d manifolds, J, Comm. Math. Phys. 175 (1996), 275-296.
22. L. Rozansky, Residue formulas for the large k asymptotics of Witten’s invariants of Seifert manifolds: The case ofSU(2 J Comm. Math. Phys. 178 (1996), 27-60.
23. L. Rozansky, Witten’s invariants of rational homology spheres at prime values of K and trivial con nection contribution, Comm. Math. Phys. 180 (1996), 297-324.
24. L. Rozansky, “On finite type invariants of links and rational homology spheres derived from the Jones polynomial and Witten-Reshetikhin-Turaev invariant” in Geometry and Physics (Aarhus, 1995), Lecture Notes in Pure and Appl. Math. 184, Dekker, New York, 1997, 379-397.
25. L. Rozansky, Higher order terms in the Melvin-Morton expansion of the colored Jones polynomial, preprint, q-alg/9601009.
26. L. Rozansky, The universal R-matrix, Burau representation, and the Melvin-Morton expansion of the colored Jones polynomial, preprint, q-alg/9604005.
27. L. Rozansky, in preparation.
28. K. Walker, An Extension of Casson’s Invariant, Ann. of Math. Stud. 126, Princeton Univ. Press, Princeton, 1992.
29. E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989), 351-399.