论文标题
$ \ mathbb {z} $上的有限繁殖统一运算符的同置类型
Homotopy type of the space of finite propagation unitary operators on $\mathbb{Z}$
论文作者
论文摘要
从数学物理学中的量子步行的角度来看，Gross，Nesme，Vogts和Werner开发了有限繁殖统一运算符的索引理论。特别是，他们证明了空间的$π_0$由索引确定。但是，对于较高的同型组，尚无任何了解。在本文中，我们描述了有限传播统一操作员在Square of Square Space of Square汇总$ \ Mathbb {C} $ - 估价$ \ Mathbb {z} $序列上的同型类型，因此我们可以确定其同质群。我们还研究（最终）周期性繁殖单一操作员的空间。
The index theory for the space of finite propagation unitary operators was developed by Gross, Nesme, Vogts and Werner from the viewpoint of quantum walks in mathematical physics. In particular, they proved that $π_0$ of the space is determined by the index. However, nothing is known about the higher homotopy groups. In this article, we describe the homotopy type of the space of finite propagation unitary operators on the Hilbert space of square summable $\mathbb{C}$-valued $\mathbb{Z}$-sequences, so we can determine its homotopy groups. We also study the space of (end-)periodic finite propagation unitary operators.
