学術雑誌論文 Group approximation in Cayley topology and coarse geometry, III: Geometric property (T)

Mimura, Masato  ,  Ozawa, Narutaka  ,  Sako, Hiroki  ,  Suzuki, Yuhei

15 ( 2 )  , pp.1067 - 1091 , 2015-04-22 , Math­em­at­ic­al So­ci­ety Pub­lish­ing
ISSN:1472-2747
NII書誌ID(NCID):AA11963392
内容記述
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.
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http://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/198462/1/agt.2015.15.1067.pdf

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