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1 November 2004 Integrality for TQFTs
Patrick M. Gilmer
Duke Math. J. 125(2): 389-413 (1 November 2004). DOI: 10.1215/S0012-7094-04-12527-8

Abstract

We discuss ways that the ring of coefficients for a topological quantum field theory (TQFT) can be reduced if one restricts somewhat the allowed cobordisms. When we apply these methods to a TQFT associated to SO(3) at an odd prime p, we obtain a functor from a somewhat restricted cobordism category to the category of free finitely generated modules over a ring of cyclotomic integers: ℤ[ζ2p] if p≡−1 (mod 4), and ℤ[ζ4p] if p≡1 (mod 4), where ζk is a primitive kth root of unity. We study the quantum invariants of prime power order simple cyclic covers of 3-manifolds. We define new invariants arising from strong shift equivalence and integrality. Similar results are obtained for some other TQFTs, but the modules are guaranteed only to be projective.

Citation

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Patrick M. Gilmer. "Integrality for TQFTs." Duke Math. J. 125 (2) 389 - 413, 1 November 2004. https://doi.org/10.1215/S0012-7094-04-12527-8

Information

Published: 1 November 2004
First available in Project Euclid: 27 October 2004

zbMATH: 1107.57020
MathSciNet: MR2096678
Digital Object Identifier: 10.1215/S0012-7094-04-12527-8

Subjects:
Primary: 57M99
Secondary: 57M10

Rights: Copyright © 2004 Duke University Press

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Vol.125 • No. 2 • 1 November 2004
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