论文标题
戴维斯综合大楼的拓扑上的一组僵硬的商
A topologically rigid set of quotients of the Davis complex
论文作者
论文摘要
如果有同一基本组的两个空间也是同构的，那么一类拓扑空间在拓扑上是僵化的。拓扑刚度除了其内在的兴趣外，还可用于解决抽象的可辨别性问题。在本文中，我们通过在阻碍拓扑刚性的定义图上提供条件，探讨了某些正确角度的Coxeter群体戴维斯复合物商的拓扑刚性。此外，我们探讨了为什么戴维斯综合体的商很难实现拓扑刚性。尽管如此，我们通过引入无限的许多无限拓扑刚性的亚类来结束。
A class of topological spaces is topologically rigid if any two spaces with the same fundamental group are also homeomorphic. Topological rigidity, in addition to its intrinsic interest, has been useful for solving abstract commensurability questions. In this paper, we explore the topological rigidity of quotients of the Davis complex of certain right angled Coxeter groups by providing conditions on the defining graphs that obstruct topological rigidity. Furthermore, we explore why topological rigidity is hard to achieve for quotients of the Davis complex. Nonetheless, we conclude by introducing infinitely many infinite topologically rigid subclasses.
