当两个Coxeter orbifolds是同形的？
When are two Coxeter orbifolds diffeomorphic?
摘要：
我们可以定义一个带角的紧致流形是一个“带可收缩面的可收缩流形”。“两个组合等价的，具有可收缩面的可收缩流形是可收缩的，当且仅当它们的4维面是可收缩的。因此，两个简单的凸多胞体是组合等价的当且仅当它们是带角点的流形。另一方面，根据Akbulut的一个结果，对于每个n > 3，存在光滑的、可收缩的n-流形，其可收缩的面是组合等价的，但不是单纯的。应用给出了刚性问题的反射群和光滑环面行动。
英文摘要：
One can define what it means for a compact manifold with corners to be a "contractible manifold with contractible faces." Two combinatorially equivalent, contractible manifolds with contractible faces are diffeomorphic if and only if their 4-dimensional faces are diffeomorphic. It follows that two simple convex polytopes are combinatorially equivalent if and only if they are diffeomorphic as manifolds with corners. On the other hand, by a result of Akbulut, for each n > 3, there are smooth, contractible n-manifolds with contractible faces which are combinatorially equivalent but not diffeomorphic. Applications are given to rigidity questions for reflection groups and smooth torus actions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
