New nonlinear hyperbolic groups

TL;DR

This paper constructs new examples of nonlinear hyperbolic groups with specific properties, expanding the understanding of hyperbolic group structures using advanced algebraic techniques.

Contribution

It introduces a method to build nonlinear hyperbolic groups that are large, torsion-free, one-ended, and admit a finite K(π,1), using superrigid lattices and group extensions.

Findings

Constructed nonlinear hyperbolic groups with desired properties

Demonstrated the use of amalgamated free products and HNN extensions

Provided new examples expanding the class of known hyperbolic groups

Abstract

We construct nonlinear hyperbolic groups which are large, torsion-free, one-ended, and admit a finite $K(\pi,1)$. Our examples are built from superrigid cocompact rank one lattices via amalgamated free products and HNN extensions.