Algebraic & Geometric Topology Volume 7, issue 4 (2007)

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Congruence and quantum invariants of 3–manifolds

Patrick M Gilmer

Algebraic & Geometric Topology 7 (2007) 1767–1790

DOI: 10.2140/agt.2007.7.1767

Bibliography

1	N A’Campo, TQFT, computations and experiments, arXiv:math.GT/0312016
2	B Bakalov, A Kirillov Jr., Lectures on tensor categories and modular functors, University Lecture Series 21, American Mathematical Society (2001) MR1797619
3	P Bantay, The kernel of the modular representation and the Galois action in RCFT, Comm. Math. Phys. 233 (2003) 423 MR1962117
4	C Blanchet, N Habegger, G Masbaum, P Vogel, Three-manifold invariants derived from the Kauffman bracket, Topology 31 (1992) 685 MR1191373
5	C Blanchet, N Habegger, G Masbaum, P Vogel, Topological quantum field theories derived from the Kauffman bracket, Topology 34 (1995) 883 MR1362791
6	Q Chen, T Le, Quantum invariants of periodic links and periodic 3–manifolds, Fund. Math. 184 (2004) 55 MR2128042
7	T D Cochran, A Gerges, K Orr, Dehn surgery equivalence relations on 3–manifolds, Math. Proc. Cambridge Philos. Soc. 131 (2001) 97 MR1833077
8	T D Cochran, P Melvin, Quantum cyclotomic orders of 3–manifolds, Topology 40 (2001) 95 MR1791269
9	M K Dabkowski, J H Przytycki, Unexpected connections between Burnside groups and knot theory, Proc. Natl. Acad. Sci. USA 101 (2004) 17357 MR2110443
10	R H Fox, Congruence classes of knots, Osaka Math. J. 10 (1958) 37 MR0131871
11	M Freedman, V Krushkal, On the asymptotics of quantum $\mathrm{SU}(2)$ representations of mapping class groups, Forum Math. 18 (2006) 293 MR2218422
12	T Gannon, Moonshine beyond the Monster, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2006) MR2257727
13	P M Gilmer, On the Witten–Reshetikhin–Turaev representations of mapping class groups, Proc. Amer. Math. Soc. 127 (1999) 2483 MR1487369
14	P M Gilmer, Integrality for TQFTs, Duke Math. J. 125 (2004) 389 MR2096678
15	P Gilmer, G Masbaum, Integral lattices in TQFT, Ann. Sci. École Norm. Sup. (to appear)
16	P M Gilmer, G Masbaum, P van Wamelen, Integral bases for TQFT modules and unimodular representations of mapping class groups, Comment. Math. Helv. 79 (2004) 260 MR2059432
17	R E Gompf, A I Stipsicz, 4–manifolds and Kirby calculus, Graduate Studies in Mathematics 20, American Mathematical Society (1999) MR1707327
18	N Jacobson, Basic algebra II, W H Freeman and Company (1989) MR1009787
19	L H Kauffman, S L Lins, Temperley–Lieb recoupling theory and invariants of 3–manifolds, Annals of Mathematics Studies 134, Princeton University Press (1994) MR1280463
20	M Lackenby, Fox's congruence classes and the quantum–$\mathrm{SU}(2)$ invariants of links in 3–manifolds, Comment. Math. Helv. 71 (1996) 664 MR1420515
21	S Lang, $\mathrm{SL}_{2}(\mathbb{R})$, Addison–Wesley (1975) MR0430163
22	M Larsen, Z Wang, Density of the SO(3) TQFT representation of mapping class groups, Comm. Math. Phys. 260 (2005) 641 MR2183960
23	W B R Lickorish, The unknotting number of a classical knot, from: "Combinatorial methods in topology and algebraic geometry (Rochester, N.Y., 1982)", Contemp. Math. 44, Amer. Math. Soc. (1985) 117 MR813107
24	G Masbaum, J D Roberts, On central extensions of mapping class groups, Math. Ann. 302 (1995) 131 MR1329450
25	G Masbaum, J D Roberts, A simple proof of integrality of quantum invariants at prime roots of unity, Math. Proc. Cambridge Philos. Soc. 121 (1997) 443 MR1434653
26	J Milnor, On the 3–dimensional Brieskorn manifolds $M(p,q,r)$, from: "Knots, groups, and 3-manifolds (Papers dedicated to the memory of R. H. Fox)", Ann. of Math. Studies 84, Princeton Univ. Press (1975) 175 MR0418127
27	J M Montesinos, Seifert manifolds that are ramified two-sheeted cyclic coverings, Bol. Soc. Mat. Mexicana $(2)$ 18 (1973) 1 MR0341467
28	H Murakami, Quantum $\mathrm{SO}(3)$–invariants dominate the $\mathrm{SU}(2)$–invariant of Casson and Walker, Math. Proc. Cambridge Philos. Soc. 117 (1995) 237 MR1307078
29	M Neuhauser, An explicit construction of the metaplectic representation over a finite field, J. Lie Theory 12 (2002) 15 MR1885034
30	PARI/GP, version 2.1.6 (2005)
31	V G Turaev, Quantum invariants of knots and 3–manifolds, de Gruyter Studies in Mathematics 18, Walter de Gruyter & Co. (1994) MR1292673
32	S Wolfram, The Mathematica book, Wolfram Media, Champaign, IL (1999) MR1721106