Integral lattices in TQFT

 Access to full text

 Full (PDF)

1. [1] Bar-Natan D., Knot Atlas, http://www.math.toronto.edu/~drorbn/KAtlas/index.html. 
2. [2] Beliakova A., Le T.T.Q., Integrality of quantum 3-manifold invariants and rational surgery formula, math.GT/0608627. Zbl1138.57014
3. [3] Blanchet C., Habegger N., Masbaum G., Vogel P., Topological quantum field theories derived from the Kauffman bracket, Topology34 (1995) 883-927. Zbl0887.57009MR1362791
4. [4] Cochran T., Melvin P., Quantum cyclotomic orders of 3-manifolds, Topology40 (1) (2001) 95-125. Zbl0997.57024MR1791269
5. [5] Chen Q., On certain integral tensor categories and integral TQFTs, math.QA/0408356. Zbl1317.81236
6. [6] Chen Q., Le T., Almost integral TQFTs from simple Lie algebras, Algebr. Geom. Topol.5 (2005) 1291-1314. Zbl1089.57020MR2171810
7. [7] Frohman C., Kania-Bartoszynska J., A quantum obstruction to embedding, Math. Proc. Cambridge Philos. Soc.131 (2001) 279-293. Zbl0991.57023MR1857120
8. [8] Gilmer P., Integrality for TQFTs, Duke Math J.125 (2) (2004) 389-413. Zbl1107.57020MR2096678
9. [9] Gilmer P., On the Frohman Kania-Bartoszynska ideal, Math. Proc. Cambridge Philos. Soc.141 (2006) 265-271. Zbl1181.57013MR2265873
10. [10] Gilmer P., Masbaum G., van Wamelen P., Integral bases for TQFT modules and unimodular representations of mapping class groups, Comment. Math. Helv.79 (2004) 260-284. Zbl1055.57026MR2059432
11. [11] Gilmer P., Qazaqzeh K., The parity of the Maslov index and the even cobordism category, Fund. Math.188 (2005) 95-102. Zbl1157.57303MR2191941
12. [12] Harvey S., On the cut number of a 3-manifold, Geom. Topol.6 (2002) 409-424. Zbl1021.57006MR1928841
13. [13] Jaco W., Geometric realizations for free quotients, J. Austral. Math. Soc.14 (1972) 411-418. Zbl0259.57004MR316571
14. [14] Kauffman L.H., Lins S., Temperley–Lieb Recoupling Theory and Invariants of 3-Manifolds, Annals of Mathematics Studies, vol. 134, Princeton University Press, 1994. Zbl0821.57003
15. [15] Kerler T., p-modular TQFT's, Milnor torsion and the Casson–Lescop invariant, Geom. Topol. Monogr.4 (2002) 119-141. Zbl1013.57018
16. [16] Le T.T.Q., Strong integrality of quantum invariants of 3-manifolds, Trans. AMS, in press, math.GT/0512433. 
17. [17] Leininger C., Reid A., The co-rank conjecture for 3-manifold groups, Algebr. Geom. Topol.2 (2002) 37-50. Zbl0983.57001MR1885215
18. [18] Masbaum G., in preparation. 
19. [19] Masbaum G., Roberts J., A simple proof of integrality of quantum invariants at prime roots of unity, Math. Proc. Cambridge Philos. Soc.121 (3) (1997) 443-454. Zbl0882.57010MR1434653
20. [20] Masbaum G., Vogel P., 3-valent graphs and the Kauffman bracket, Pacific J. Math.164 (1994) 361-381. Zbl0838.57007MR1272656
21. [21] Masbaum G., Wenzl H., Integral modular categories and integrality of quantum invariants at roots of unity of prime order, J. reine angew. Math. (Crelle's Journal)505 (1998) 209-235. Zbl0919.57010MR1662260
22. [22] Murakami H., Quantum $\mathrm{SO}\left(3\right)$-invariants dominate the $\mathrm{SU}\left(2\right)$-invariant of Casson and Walker, Math. Proc. Cambridge Philos. Soc.117 (2) (1995) 237-249. Zbl0854.57016MR1307078
23. [23] Ohtsuki T., A polynomial invariant of rational homology 3-spheres, Invent. Math.123 (2) (1996) 241-257. Zbl0855.57016MR1374199
24. [24] Reiner I., Maximal Orders, London Mathematical Society Monographs, vol. 5, Academic Press, London–New York, 1975. Zbl1024.16008
25. [25] Reshetikhin N., Turaev V., Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math.103 (1991) 547-597. Zbl0725.57007MR1091619
26. [26] Stallings J., Problems about free quotients of groups, in: Geometric Group Theory, Columbus, OH, 1992, Ohio State Univ. Math. Res. Inst. Publ., vol. 3, de Gruyter, Berlin, 1995, pp. 165-182. Zbl0869.20012MR1355111
27. [27] Sikora A., Cut numbers of 3-manifolds, Trans. AMS357 (5) (2005) 2007-2020. Zbl1064.57018MR2115088
28. [28] Turaev V.G., Quantum Invariants of Knots and 3-Manifolds, de Gruyter, 1994. Zbl0812.57003MR1292673
29. [29] Walker K., On Witten's 3-manifold invariants, Preprint, 1991, http://canyon23.net/math/.