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A further classification of the boundaries of the Croke-Kleiner Group.

机译：Croke-Kleiner集团边界的进一步分类。

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摘要

In the category of CAT(0) groups, the Croke-Kleiner group holds special prominence as the first known non-rigid CAT(0) group. Further, it has served as the example from which all other currently known non-rigid CAT(0) groups have been created. Despite this, much still remains unclear about the various boundaries of the Croke-Kleiner group itself. Conditions have been given by J. Wilson that will ensure two boundaries are nonhomeomorphic, and on the other extreme, B. Croke and C. Kleiner have found conditions that are necessary and sufficient for the boundary of two spaces to be G-equivariantly homeomorphic. This dissertation aims to address the gap between these two extremes by introducing a notion of isovariantly homeomorphic and giving some conditions necessary for two boundaries of the Croke-Kleiner group to be isovariantly homeomorphic. Examples of non-G-equivariantly homeomorphic, but still isovariantly homeomorphic, boundaries are described using Dehn twists and other automorphisms of the Croke-Kleiner group.
机译：在CAT（0）组类别中，Croke-Kleiner组作为第一个已知的非刚性CAT（0）组尤为突出。此外，它作为创建所有其他当前已知的非刚性CAT（0）组的示例。尽管如此，对于Croke-Kleiner集团本身的各个界限仍然不清楚。 J. Wilson给出了确保两个边界为非同胚的条件，而在另一个极端，B。Croke和C. Kleiner发现了两个空间的边界为G同等同胚的必要条件和充分条件。本论文旨在通过引入等变同胚的概念，并给出Croke-Kleiner群的两个边界为等变同胚的必要条件，来解决这两个极端之间的鸿沟。使用Dehn扭曲和Croke-Kleiner组的其他自同构描述了非G等距同胚但仍等同同胚的边界的示例。

著录项

  • 作者

    Fonstad, Paul.;

  • 作者单位

    The University of Wisconsin - Milwaukee.;

  • 授予单位 The University of Wisconsin - Milwaukee.;
  • 学科 Mathematics.
  • 学位 Ph.D.
  • 年度 2012
  • 页码 62 p.
  • 总页数 62
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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