TY - JOUR
T1 - Group approximation in cayley topology and coarse geometry, III
T2 - Geometric property (T)
AU - Mimura, Masato
AU - Ozawa, Narutaka
AU - Sako, Hiroki
AU - Suzuki, Yuhei
N1 - Publisher Copyright:
© 2015, Algebraic & Geometric Topology. All Rights Reserved.
PY - 2015/4/22
Y1 - 2015/4/22
N2 - 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.
AB - 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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U2 - 10.2140/agt.2015.15.1067
DO - 10.2140/agt.2015.15.1067
M3 - Article
AN - SCOPUS:84928981303
VL - 15
SP - 1061
EP - 1091
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
SN - 1472-2747
IS - 2
ER -