拓扑量子场论与强位移等价
Topological Quantum Field Theory And Strong Shift Equivalence
摘要：
给定一个d+1维的TQFT和一个闭（d+1）维流形M的无限循环覆盖，我们定义了一个取值于矩阵的强移位等价类的不变量.强移位等价的概念起源于R。威廉姆斯在符号动力学方面的工作。与TQFT和无限循环覆盖相关联的Turaev-Viro模则由该矩阵远离零的Jordan形式给出。如果M的边界有一个圆因子，并且边界的无限循环覆盖是标准的，则也定义了这个不变量。我们定义了一个变体的TQFT相关的有限群G已研究奎因。通过这种方式，我们恢复了由于D的链接不变量。Silver和S.威廉姆斯我们还获得了一个变化的Silver-Williams不变量，通过使用TQFT与G在其未修改的形式。
英文摘要：
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.
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