## Duke Mathematical Journal

### Integrality for TQFTs

Patrick M. Gilmer

#### 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.

#### Article information

Source
Duke Math. J., Volume 125, Number 2 (2004), 389-413.

Dates
First available in Project Euclid: 27 October 2004

https://projecteuclid.org/euclid.dmj/1098892274

Digital Object Identifier
doi:10.1215/S0012-7094-04-12527-8

Mathematical Reviews number (MathSciNet)
MR2096678

Zentralblatt MATH identifier
1107.57020

Subjects
Primary: 57M99: None of the above, but in this section
Secondary: 57M10: Covering spaces

#### Citation

Gilmer, Patrick M. Integrality for TQFTs. Duke Math. J. 125 (2004), no. 2, 389--413. doi:10.1215/S0012-7094-04-12527-8. https://projecteuclid.org/euclid.dmj/1098892274

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