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 a reduced irreducible classical root system of rank at least 2, and ME analogues of such groups, into an acylindrically hyperbolic group has an absolutely elliptic image. This result provides a non-arithmetic generalization of homomorphism superrigidity of Farb–Kaimanovich–Masur and Bridson–Wade