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Licensed Unlicensed Requires Authentication Published by De Gruyter March 1, 2011

Quasi-homomorphism rigidity with non-commutative targets

  • Narutaka Ozawa EMAIL logo

Abstract

As a strengthening of Kazhdan's property (T) for locally compact groups, property (TT) was introduced by Burger and Monod. In this paper, we add more rigidity and introduce property (TTT). This property is suited for the study of rigidity phenomena for quasi-homomorphisms with non-commutative targets. Partially upgrading a result of Burger and Monod, we will prove that SLn(ℝ) with n ≧ 3 and their lattices have property (TTT). As a corollary, we generalize the well-known fact that every homomorphism from such a lattice into an amenable group or a hyperbolic group has finite image to the extent that it includes a quasi-homomorphism.

Received: 2010-01-09
Revised: 2010-02-15
Published Online: 2011-03-01
Published in Print: 2011-June

© Walter de Gruyter Berlin · New York 2011

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