Geometric property (T)
By Rufus Willett, Guoliang Yu. 2013
48 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/58385045b4facc5143af2319ac6fc03d76c713f1
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In Algebra and Number Theory
In Applied Mathematics
In Mathematical Physics
- Rufus Willett
- E. Guentner
- P. Baum
- Guoliang Yu
- Martin Finn-Sell
- Nathanial P. Brown Narutaka Ozawa
- N. Higson
- Ján Špakula
Citations in the corpus
- Expanders, exact crossed products, and the Baum–Connes conjecture (2013, background): “groups and group actions. It is crucial here that the only expanders anyone knows how to coarsely embed into a group are those with ‘large girth’, as we exploited in Section 7. In [53, Section 7] and [54], Yu and the third author study a property of expanders called geometric property (T), which is ”