Abstract
AbstractGiven a TQFT in dimensiond+ 1; and an infinite cyclic covering of a closed (d+ 1)-dimensional manifoldM, 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 ofMhas anS1factor and the infinite cyclic cover of the boundary is standard. We define a variant of a TQFT associated to a finite groupGwhich 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 toGin its unmodified form.
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