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Group approximation in
Cayley topology and coarse geometry, III: Geometric property
$\mathrm{(T)}$
Masato Mimura, Narutaka Ozawa, Hiroki Sako and Yuhei Suzuki |
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Algebraic & Geometric Topology 15 (2015) 1067–1091
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Abstract |
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In this series of papers, we study the correspondence between the following: (1) the large scale structure of the metric space consisting of Cayley graphs of finite groups with generators; (2) the structure of groups that appear in the boundary of the set in the space of –marked groups. In this third part of the series, we show the correspondence among the metric properties “geometric property ”, “cohomological property ” and the group property “Kazhdan’s property ”. Geometric property of Willett–Yu is stronger than being expander graphs. Cohomological property is stronger than geometric property for general coarse spaces. |
Keywords
coarse geometry, geometric property $\mathrm{(T)}$, space
of marked groups, coarse cohomology
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Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 46M20
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References |
Publication
Received: 21 May 2014
Accepted: 26 August 2014
Published: 22 April 2015
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Authors |
| Masato Mimura | |
| Mathematical Institute Tohoku University Sendai 980-8578 Japan |
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| http://www.math.tohoku.ac.jp/~mimura/index.html | |
| Narutaka Ozawa | |
| Research Institute for Mathematical
Sciences Kyoto University Kyoto 606-8502 Japan |
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| http://www.kurims.kyoto-u.ac.jp/~narutaka/ | |
| Hiroki Sako | |
| School of Science Tokai University Hiratsuka 259-1292 Japan |
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| http://www1.hinocatv.ne.jp/sako-h/research/research.html | |
| Yuhei Suzuki | |
| Department of Mathematical
Sciences University of Tokyo Tokyo 153-0041 Japan |
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| http://www.ms.u-tokyo.ac.jp/~suzukiyu/ | |
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