Quantum invariants of 3-manifolds: Integrality, splitting, and perturbative expansion

Topology and its Applications

Volumn 127, Issue 1-2, 2003, Pages 125-152

  Le, Thang T Q ^a  

^a UNIVERSITY AT BUFFALO   (United States)

Author keywords

3 manifolds; Homology spheres; Quantum invariants; Simple Lie algebras

Indexed keywords

EID: 0038012561     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-8641(02)00056-1     Document Type: Article

References (20)

1. Andersen H. Paradowski J. Fusion categories arising from semisimple Lie algebra Comm. Math. Phys. 169 1995 563-588
2. Deloup F. Linking form, Reciprocity for Gauss sums and invariants of 3-manifolds Trans. Amer. Math. Soc. 351 1999 1859-1918
3. IKassel C. Quantum Groups in: Graduate Text in Math. 155 1995 Springer-Verlag New York
4. Kirillov A. On an inner product in modular categories J. Amer. Math. Soc. 9 1996 1135-1169
5. Kirby R. Melvin P. The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2,ℂ) Invent. Math. 105 1991 473-545
6. Kohno T. Takata T. Level-rank duality for Witten's 3-manifold invariant Progress in Algebraic Combinatorics Adv. Stud. Pure Math. 24 1996 243-264
7. R. Lawrence, D. Zagier, Modular forms and quantum invariants of 3-manifolds, Preprint, 1999
8. T.T.Q. Le, On perturbative PSU(n) invariants of rational homology 3-spheres, Topology, to appear
9. Le T.T.Q. Integrality and symmetry of quantum link invariants Duke Math. J. 102 2000 273-306
10. Le T.T.Q. Murakami J. The universal Vassiliev-Kontsevich invariant for framed oriented links Compositio Math. 102 1996 41-64
11. Lusztig G. Introduction to Quantum Groups 1993 Birkhäuser Basel
12. Masbaum G. Roberts J. A simple proof of integrality of quantum invariants at prime roots of unity Math. Proc. Cambridge Philos. Soc. 121 1997 443-454
13. Masbaum G. Wenzl H. Integral modular categories and integrality of quantum invariants at roots of unity of prime order J. Reine Angew. Math. 505 1998 209-235
14. Murakami H. Quantum SO(3)-invariants dominate the SU(2)-invariant of Casson and Walker Math. Proc. Cambridge Philos. Soc. 117 1995 237-249
15. Murakami H. Ohtsuki T. Okada M. Invariants of 3-manifolds derived from linking matrices of framed links Osaka J. Math. 29 1992 545-572
16. Ohtsuki T. A polynomial invariant of rational homology 3-spheres Invent. Math. 123 2 1996 241-257
17. Rozansky L. Witten's invariants of rational homology 3-spheres at prime values of K and trivial connection contribution Commun. Math. Phys. 180 1996 297-324
18. Sawin S. Jones-Witten invariants for non-simply connected Lie groups and the geometry of the Weyl alcove math.QA/9905010
19. Takata T. Yokota Y. The PSU(n) invariants of 3-manifolds are polynomials J. Knot Theory Ramifications 8 4 1999 521-532
20. Turaev V.G. Quantum Invariants of Knots and 3-Manifolds de Gruyter Stud. in Math. 18 1994 de Gruyter Berlin