Integrality for TQFTs
By Patrick M. Gilmer. 2001
46 citations recorded by the source corpus.
We discuss ways that the ring of coefficients for a 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 only guaranteed to be projective.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ca7abadc8b03674f9dff646f8ebe9afd63c51a9a
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In Geometry and Topology
- Kazuo Habiro
- Gregor Masbaum
- Stavros Garoufalidis
- Kazuhiro Hikami
- P. Teichner
- G. Massuyeau
- Benson Farb
- Tim D. Cochran
In Mathematical Physics
- Kazuo Habiro
- Gregor Masbaum
- Patrick M. Gilmer
- Stavros Garoufalidis
- P. Teichner
- Benson Farb
- Tim D. Cochran
- James F. Conant
Citations in the corpus
- A unified Witten–Reshetikhin–Turaev invariant for integral homology spheres (2006, background): “It is expected that the functor J̄ would lead to some refinements of the integral structures in topological quantum field theories [9, 11, 10].”
- Integral lattices in TQFT (2004, methodology): “Based on integrality results for the quantum SO(3)-invariant of closed oriented 3-manifolds [22,19], an integral TQFT-functor Sp was defined in [8] and [10].”