Hyperbolicity of T(6) Cyclically Presented Groups

TL;DR

This paper classifies when certain cyclically presented groups with specific small cancellation properties are hyperbolic, providing a complete classification in the context of T(6) conditions.

Contribution

It offers a complete classification of hyperbolic T(6) cyclically presented groups, extending existing results in geometric group theory.

Findings

Identifies conditions under which T(6) cyclically presented groups are hyperbolic.

Provides a comprehensive classification for these groups.

Extends the understanding of hyperbolicity in small cancellation groups.

Abstract

We consider groups defined by cyclic presentations where the defining word has length three and the cyclic presentation satisfies the T(6) small cancellation condition. We classify when these groups are hyperbolic. When combined with known results, this completely classifies the hyperbolic T(6) cyclically presented groups.