Topological Quantum Field Theory And Strong Shift Equivalence
Abstract
Given a TQFT in dimension d+1, and an infinite cyclic covering of a closed (d+1)-dimensional manifold M, we define an invariant taking values in a strong shift equivalence class of matrices. The notion of strong shift equivalence originated in R. Williams' work in symbolic dynamics. The Turaev-Viro module associated to a TQFT and an infinite cyclic covering is then given by the Jordan form of this matrix away from zero. This invariant is also defined if the boundary of M has a circle factor and the infinite cyclic cover of the boundary is standard. We define a variant of a TQFT associated to a finite group G which has been studied by Quinn. In this way, we recover a link invariant due to D. Silver and S. Williams. We also obtain a variation on the Silver-Williams invariant, by using the TQFT associated to G in its unmodified form.
Cite
@article{arxiv.math/9712214,
title = {Topological Quantum Field Theory And Strong Shift Equivalence},
author = {Patrick M. Gilmer},
journal= {arXiv preprint arXiv:math/9712214},
year = {2015}
}
Comments
AMS-TeX, 8 pages, a few small changes changes