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

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

  1. Rufus Willett
  2. E. Guentner
  3. Nathanial P. Brown Narutaka Ozawa

In Applied Mathematics

  1. Rufus Willett
  2. E. Guentner
  3. P. Baum
  4. Nathanial P. Brown Narutaka Ozawa

In Mathematical Physics

  1. Rufus Willett
  2. E. Guentner
  3. P. Baum
  4. Guoliang Yu
  5. Martin Finn-Sell
  6. Nathanial P. Brown Narutaka Ozawa
  7. N. Higson
  8. Ján Špakula

Citations in the corpus