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Open access
Apr, 2015

Group approximation in cayley topology and coarse geometry, III: Geometric property (T)

Algebraic and Geometric Topology
  • Masato Mimura
  • ,
  • Narutaka Ozawa
  • ,
  • Hiroki Sako
  • ,
  • Yuhei Suzuki

Volume
15
Number
2
First page
1061
Last page
1091
Language
Publishing type
Research paper (scientific journal)
DOI
10.2140/agt.2015.15.1067

In this series of papers, we study the correspondence between the following: (1) the large scale structure of the metric space ⊔m Cay (G (m) consisting of Cayley graphs of finite groups with k generators; (2) the structure of groups that appear in the boundary of the set {G (m)} in the space of k–marked groups. In this third part of the series, we show the correspondence among the metric properties “geometric property (T)”, “cohomological property (T)” and the group property “Kazhdan’s property (T)”. Geometric property .T/ of Willett–Yu is stronger than being expander graphs. Cohomological property .(T) is stronger than geometric property (T) for general coarse spaces.

Link information
DOI
https://doi.org/10.2140/agt.2015.15.1067
Scopus
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84928981303&origin=inward Open access
Scopus Citedby
https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=84928981303&origin=inward
ID information
  • DOI : 10.2140/agt.2015.15.1067
  • ISSN : 1472-2747
  • eISSN : 1472-2739
  • SCOPUS ID : 84928981303

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