Actions of right-angled Coxeter groups on the Croke–Kleiner spaces

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• 作者：Yulan Qing
• 关键词：CAT(0) space ; Right ; angled Coxeter group ; Visual boundary
• 刊名：Geometriae Dedicata
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：185
• 期：1
• 页码：1-14
• 全文大小：643 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1572-9168
• 卷排序：185

文摘

It is an open question whether right-angled Coxeter groups have unique group-equivariant visual boundaries. In Croke and Kleiner (Topology 39(3):549–556, 2000. doi:10.1016/S0040-9383(99)00016-6), presented a right-angled Artin group with more than one visual boundary. In this paper we examine the space constructed by Croke and Kleiner and present a right-angled Coxeter group that is quasi-isometric to this space. Then we change the geometric parameters of this space to show that the proposed right-angled Coxeter group has non-unique equivariant visual boundaries, hence answer the open question negatively.