## Topology & Geometric Group Theory Seminar

## Fall 2007

### 2:55 - 3:55, Malott 310D

Tuesday, October 16

**Uzy Hadad**,
Hebrew University

*Uniform Kazhdan Constant for some families of linear groups*

Let R be a ring generated by l elements with stable range r. Assume
that the group EL_{d}(R) has Kazhdan constant
ε_{0} > 0 for some d ≥ r+1. We prove that there
exist ε(ε_{0}, l) > 0 and k in **N**,
such that for every n ≥ d, EL_{n}(R) has a generating set
of order k and a Kazhdan constant larger than ε. As a
consequence, we obtain for SL_{n}(**Z**) where n ≥ 3, a
Kazhdan constant which is independent of n with respect to generating
sets of a fixed size.

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