论文标题
代币配置的离散同喻
Discrete homotopy of token configurations
论文作者
论文摘要
本文研究了拓扑中对称产品和无序配置空间的图形类似物。我们从Barcelo等人介绍的离散同义理论的角度做到这一点。我们的第一个结果是P. A. Smith定理的组合版本，该版本说，$ x $的任何非平凡对称产品的基本组都是同构至$ h_1（x）$。我们的第二个结果给出了图形的N链辫子组的条件，其离散类似物是同构的。
This paper studies graphical analogs of symmetric products and unordered configuration spaces in topology. We do so from the perspective of the discrete homotopy theory introduced by Barcelo et al. Our first result is a combinatorial version of a theorem of P. A. Smith, which says that the fundamental group of any nontrivial symmetric product of $X$ is isomorphic to $H_1(X)$. Our second result gives conditions under which the n-strand braid group of a graph is isomorphic to its discrete analog.
