Superrigidity from Chevalley groups into acylindrically hyperbolic groups via quasi-cocycles

Abstract

We prove that every homomorphism from the elementary Chevalley group over a finitely generated unital commutative ring associated with reduced irreducible classical root system of rank at least 2, and ME analogues of such groups, into acylindrically hyperbolic groups has an absolutely elliptic image. This result provides a non-arithmetic generalization of homomorphism superrigidity of Farb--Kaimanovich--Masur and Bridson--Wade.

Final version, 15 pages (v4); Accepted in J. Eur. Math. Soc., 14 pages, add comprehensive details of proofs (v3); 9 pages, Lemma 4.2 by D. Osin added (v2); 7 pages, this is the final extended version of an unpublished manuscript (arXiv:1106.3769) by the author