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

TL;DR

This paper establishes a superrigidity property for homomorphisms from elementary Chevalley groups over certain rings into acylindrically hyperbolic groups, extending known superrigidity results beyond arithmetic groups.

Contribution

It proves that such homomorphisms have an absolutely elliptic image, generalizing superrigidity results to a broader class of groups and target groups.

Findings

Homomorphisms have absolutely elliptic images.

Extends superrigidity beyond arithmetic groups.

Provides a non-arithmetic generalization of known superrigidity results.

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.