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

Masato Mimura, Narutaka Ozawa, Hiroki Sako, Yuhei Suzuki

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1061-1091
Number of pages31
JournalAlgebraic and Geometric Topology
Volume15
Issue number2
DOIs
Publication statusPublished - 2015 Apr 22

ASJC Scopus subject areas

  • Geometry and Topology

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