Integrality for TQFTS

Duke Mathematical Journal

Volumn 125, Issue 2, 2004, Pages 389-413

  Gilmer, Patrick M ^a  

^a LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 10044272961     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-04-12527-8     Document Type: Article

References (29)

1. [BHMV1] C. BLANCHET, N. HABEGGER, G. MASBAUM, and P. VOGEL, Three-manifold invariants derived from the Kauffman bracket, Topology 31 (1992), 685-699. MR 1191373
2. [BHMV2] _, Topological quantum field theories derived from the Kauffman bracket, Topology 34 (1995), 883-927. MR 1362791
3. [CL] Q. CHEN and T. LE, Quantum invariants of periodic links and periodic 3-manifolds, preprint, arXiv:math.QA/0408358
4. [CM] T. D. COCHRAN and P. MELVIN, Quantum cyclotomic orders of 3-manifolds, Topology 40 (2001), 95-125. MR 1791269
5. [G1] P. M. GILMER, Invariants for one-dimensional cohomology classes arising from TQFT, Topology Appl. 75 (1997), 217-259. MR 1430088
6. [G2] _, "Turaev-Viro modules of satellite knots" in Knots '96 (Tokyo, 1996), World Sci., River Edge, N.J., 1997, 337-363. MR 1664973
7. [G3] _, On the Witten-Reshetikhin-Turaev representations of mapping class groups, Proc. Amer. Math. Soc. 127 (1999), 2483-2488. MR 1487369
8. [G4] _, "Quantum invariants of periodic three-manifolds" in Proceedings of the Kirbyfest (Berkeley, 1998), Geom. Topol. Monogr. 2, Geom. Topol. Publ., Coventry, United Kingdom, 1999, 157-175. MR 1734407
9. [G5] _, Topological quantum field theory and strong shift equivalence, Canad. Math. Bull. 42 (1999), 190-197. MR 1692009
10. [GKP] P. M. GILMER, J. KANIA-BARTOSZYŃSKA, and J. H. PRZYTYCKI, 3-manifold invariants and periodicity of homology spheres, Algebr. Geom. Topol. 2 (2002), 825-842. MR 1936972
11. [GM] P. GILMER and G. MASBAUM, Integral lattices in TQFT, in preparation.
12. [GMV] P. M. GILMER, G. MASBAUM, and P. VAN WAMELEN, Integral bases for TQFT modules and unimodular representations of mapping class groups. Comment. Math. Helv. 79 (2004), 260-284. MR 2059432
13. [H] F. HIRZEBRUCH, "The signature theorem: Reminiscences and recreation" in Prospects in Mathematics (Princeton, 1970), Ann. of Math Stud. 70, Princeton Univ. Press, Princeton, 1971, 3-31. MR 0368023
14. [J] W. JACO, Geometric realizations for free quotients, J. Austral. Math. Soc. 14 (1972), 411-418. MR 0316571
15. [Ja] N. JACOBSON, Basic Algebra, II, 2nd ed., Freeman, New York, 1989. MR 1009787
16. [K] U. KAISER, Link Theory in Manifolds, Lecture Notes in Math. 1669, Springer, Berlin, 1997. MR 1479639
17. [L] T. T. Q. LE, "Quantum invariants of 3-manifolds: Integrality, splitting, and perturbative expansion" in Proceedings of the Pacific Institute for the Mathematical Sciences Workshop "Invariants of Three-Manifolds (Calgary, Alberta, 1999), Topology Appl. 127 (2003), 125-152. MR 1953323
18. [LM] D. LIND and B. MARCUS, An Introduction to Symbolic Dynamics and Coding, Cambridge Univ. Press, Cambridge, 1995. MR 1369092
19. 2 in free groups, Michigan Math. J. 6 (1959), 89-95. MR 0103218
20. [MR] G. MASBAUM and J. D. ROBERTS, A simple proof of integrality of quantum invariants at prime roots of unity, Math. Proc. Cambridge Philos. Soc. 121 (1997), 443-454. MR 1434653
21. [MW] G. MASBAUM and H. WENZL, Integral modular categories and integrality of quantum invariants at roots of unity of prime order, J. Reine Angew. Math. 505 (1998), 209-235. MR 1662260
22. [Mu1] H. MURAKAMI, Quantum SU(2)-invariants dominate Casson's SU(2)-invariant, Math. Proc. Cambridge Philos. Soc. 115 (1994), 253-281. MR 1277059
23. [Mu2] _, Quantum SO(3)-invariants dominate the SU(2)-invariant of Casson and Walker, Math. Proc. Cambridge Philos. Soc. 117 (1995), 237-249. MR 1307078
24. [QG] K. QAZAQZEH and P. M. GILMER, The parity of the Maslov index and the even cobordism category, preprint, arXiv:math.GT/0401135
25. [R] P. RIBENBOIM, Algebraic Numbers, Pure Appl. Math. 27, Wiley-Interscience, New York, 1972. MR 0340212
26. [TY] T. TAKATA and Y. YOKOTA, The PSU(N) invariants of 3-manifolds are algebraic integers. Jour. Knot Theory Ramifications 8 (1999), 521-532. MR 1697388
27. [T] V. G. TURAEV, Quantum Invariants of Knots and 3-Manifolds, de Gruyter Stud. Math. 18, de Gruyter, Berlin, 1994. MR 1292673
28. [W] J. B. WAGONER, Strong shift equivalence theory and the shift equivalence problem, Bull. Amer. Math. Soc. (N.S.) 36 (1999), 271-296. MR 1688990
29. [Wa] K. WALKER, On Witten's 3-manifold invariants, preprint, 1991, http://canyon23.net/math/