Asymptotic cones and boundaries of CAT(0) spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.1512/IUMJ.2021.70.8552

Curtis Kent, Russell Ricks

引用次数: 3

Abstract

We explore the relationships between the asymptotic cones of a CAT(0) space and its boundary under both the standard visual (i.e. cone) topology and the Tits metric. We show that the set of asymptotic cones of a proper cocompact CAT(0) space admits canonical connecting maps under which the direct limit is isometric to the Euclidean cone on the Tits boundary. We also demonstrate how maps between asymptotic cones induce maps between Tits boundaries, which we use to show that virtually free Abelian groups are exactly the CAT(0) groups with compact Tits boundary.

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CAT(0)空间的渐近锥与边界

我们研究了CAT(0)空间在标准视觉(即锥)拓扑和Tits度量下的渐近锥与边界之间的关系。证明了固有紧CAT(0)空间的渐近锥集允许正则连接映射，其直接极限与Tits边界上的欧几里得锥等距。我们还证明了渐近锥之间的映射如何诱导Tits边界之间的映射，我们用它来证明几乎自由的阿贝尔群正是具有紧Tits边界的CAT(0)群。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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