Quasi-homomorphism rigidity with noncommutative targets

Details Quasi-homomorphism rigidity with noncommutative targets Quasi-homomorphism rigidity with noncommutative targets

2009-11-20

arxiv.org/abs/0911.3975v4

Mathematics

Group Theory

18 pages; Minor modification (v2); The abstract and introduction beefed up (v3); An error in the proof of Proposition 3 fixed

Scientific paper

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 noncommutative targets. Partially upgrading a result of Burger and Monod, we will prove that SL(n,R) with n at least 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.

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