|
|
| |
| Geometric Property (T) |
| |
Citation： |
Rufus WILLETT,Guoliang YU.Geometric Property (T)[J].Chinese Annals of Mathematics B,2014,35(5):761~800 |
| Page view： 1190
Net amount： 960 |
Authors： |
Rufus WILLETT; Guoliang YU; |
Foundation： |
the U.S. National Science Foundation (Nos.DMS1229939, DMS1342083,
DMS1362772). |
|
|
| Abstract： |
This paper discusses “geometric property (T)”. This is a property of metric
spaces introduced in earlier works of the authors for its applications to K-theory. Geometric
property (T) is a strong form of “expansion property”, in particular, for a sequence (Xn)
of bounded degree finite graphs, it is strictly stronger than (Xn) being an expander in the
sense that the Cheeger constants h(Xn) are bounded below.
In this paper, the authors show that geometric property (T) is a coarse invariant,
i.e., it depends only on the large-scale geometry of a metric space X. The authors also
discuss how geometric property (T) interacts with amenability, property (T) for groups,
and coarse geometric notions of a-T-menability. In particular, it is shown that property
(T) for a residually finite group is characterised by geometric property (T) for its finite
quotients. |
Keywords： |
Coarse geometry, Expander, Roe algebra, Property (T) |
Classification： |
20F69, 46L85, 51F99 |
|
|
Download PDF Full-Text
|
|
|
|
