Topological Quantum Field Theory and Strong Shift Equivalence
نویسندگان
چکیده
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 S 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. This version:(1 /12 /98); First version: (7 /3 /97)
منابع مشابه
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This paper discusses strong shift equivalence and counterexamples to the long standing Shift Equivalence Problem in symbolic dynamics. We also discuss how strong shift equivalence theory is closely related to areas of mathematics outside dynamics such as algebraic K-theory, cyclic homology, and topological quantum field theory.
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