Lp-compression of wreath products and some related groups
Presenter
December 9, 2016
Keywords:
- wreath product
- Lp-compression
- amenable groups
- a-T-menability
- fixed point properties
- hyperbolic groups and generalizations
- Banach space
- group cohomology
- expander graph
- index theory
- non-commutative geometry
MSC:
- 20F65
- 22D10
- 20-xx
- 43-xx
- 46-xx
- 57-xx
- 58-xx
- 19-xx
- 46L80
- 20J06
- 43A07
Abstract
We show a formula relating the L_p-compression exponent of a group and its wreath product with a cyclic group for p in [1, 2]. The argument extends the Markov type method introduced by Naor and Peres. Using wreath product as ingredients, we construct finitely generated amenable groups with arbitrary prescribed L_p compression exponent in the interval [0,1]. This can be viewed as an elementary amenable analogue of a result of Arzhantseva, Drutu and Sapir. Joint with Jeremie Brieussel