Topological Quantum Field Theory and Strong Shift Equivalence

Canadian mathematical bulletin

关键词: knot;    link;    TQFT;    symbolic dynamics;    shift equivalence;   

DOI  :  10.4153/CMB-1999-023-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Given a TQFT in dimension $d+1,$ and an infinite cyclic covering ofa closed $(d+1)$-dimensional manifold $M$, we define an invarianttaking values in a strong shift equivalence class of matrices. Thenotion of strong shift equivalence originated in R.~Williams' workin symbolic dynamics. The Turaev-Viro module associated to a TQFTand an infinite cyclic covering is then given by the Jordan form ofthis matrix away from zero. This invariant is also defined if theboundary of $M$ has an $S^1$ factor and the infinite cyclic coverof the boundary is standard. We define a variant of a TQFTassociated to a finite group $G$ which has been studied by Quinn.In this way, we recover a link invariant due to D.~Silver andS.~Williams. We also obtain a variation on the Silver-Williamsinvariant, by using the TQFT associated to $G$ in its unmodified form.

【 授权许可】

Unknown