Superrigidity from Chevalley groups into acylindrically hyperbolic groups via quasi-cocycles
Group Theory
2018-01-29 v4 Geometric Topology
K-Theory and Homology
Rings and Algebras
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.
Cite
@article{arxiv.1502.03703,
title = {Superrigidity from Chevalley groups into acylindrically hyperbolic groups via quasi-cocycles},
author = {Masato Mimura},
journal= {arXiv preprint arXiv:1502.03703},
year = {2018}
}
Comments
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details of proofs (v3); 9 pages, Lemma 4.2 by D. Osin added (v2); 7 pages, this is the final extended version of an unpublished manuscript (arXiv:1106.3769) by the author