Almost integral TQFTs from simple Lie algebras
Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1291-1314
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Almost integral TQFTs were introduced by Gilmer [Duke Math. J. 125 (2004) 389–413]. The aim of this paper is to modify the TQFT of the category of extended 3–cobordisms given by Turaev (in his book: Quantum invariants of knots and 3–manifolds) to obtain an almost integral TQFT.

DOI : 10.2140/agt.2005.5.1291
Keywords: TQFT, almost integral TQFT, simple Lie algebra

Chen, Qi  1   ; Le, Thang T Q  2

1 Department of Mathematics, The Ohio State University, Columbus OH 43210-1174, USA
2 School of Mathematics, Georgia Institute of Technology, Atlanta GA 30332-0160, USA
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Chen, Qi; Le, Thang T Q. Almost integral TQFTs from simple Lie algebras. Algebraic and Geometric Topology, Tome 5 (2005) no. 4, pp. 1291-1314. doi: 10.2140/agt.2005.5.1291

[1] B Bakalov, A Kirillov Jr., Lectures on tensor categories and modular functors, University Lecture Series 21, American Mathematical Society (2001)

[2] C Blanchet, N Habegger, G Masbaum, P Vogel, Topological quantum field theories derived from the Kauffman bracket, Topology 34 (1995) 883

[3] N Bourbaki, Lie groups and Lie algebras. Chapters 1–3, Elements of Mathematics (Berlin), Springer (1989)

[4] Q Chen, On certain integral tensor categories and integral TQFTs

[5] Q Chen, T Le, Quantum invariants of periodic links and periodic 3–manifolds, Fund. Math. 184 (2004) 55

[6] P M Gilmer, J Kania-Bartoszynska, J H Przytycki, 3–manifold invariants and periodicity of homology spheres, Algebr. Geom. Topol. 2 (2002) 825

[7] P M Gilmer, Integrality for TQFTs, Duke Math. J. 125 (2004) 389

[8] C Kassel, Quantum groups, Graduate Texts in Mathematics 155, Springer (1995)

[9] C Kassel, V Turaev, Chord diagram invariants of tangles and graphs, Duke Math. J. 92 (1998) 497

[10] A A Kirillov Jr., On an inner product in modular tensor categories, J. Amer. Math. Soc. 9 (1996) 1135

[11] T T Q Le, On perturbative $\mathrm{PSU}(n)$ invariants of rational homology 3–spheres, Topology 39 (2000) 813

[12] T T Q Le, Quantum invariants of 3–manifolds: integrality, splitting, and perturbative expansion, from: "Proceedings of the Pacific Institute for the Mathematical Sciences Workshop “Invariants of Three–Manifolds” (Calgary, AB, 1999)" (2003) 125

[13] T Q T Le, J Murakami, The universal Vassiliev–Kontsevich invariant for framed oriented links, Compositio Math. 102 (1996) 41

[14] G Lusztig, Introduction to quantum groups, Progress in Mathematics 110, Birkhäuser (1993)

[15] N Reshetikhin, V G Turaev, Invariants of 3–manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991) 547

[16] V G Turaev, Quantum invariants of knots and 3–manifolds, de Gruyter Studies in Mathematics 18, Walter de Gruyter Co. (1994)

[17] G Warner, Harmonic analysis on semi-simple Lie groups I, Grundlehren der mathematischen Wissenschaften 188, Springer (1972)

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