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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Quasi-homomorphism rigidity with non-commutative targets

1Department of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo, 153-8914, Japan

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2011, Issue 655, Pages 89–104, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crelle.2011.034, March 2011

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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.

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