All hyperbolic cyclically presented groups with positive length three relators

Abstract

We consider the cyclically presented groups defined by cyclic presentations with $2m$ generators $x_i$ whose relators are the $2m$ positive length three relators $x_i{x}_{i+1}{x}_{i+m-1}$. We show that they are hyperbolic if and only if $m\in \{1,2,3,6,9\}$. This completes the classification of the hyperbolic cyclically presented groups with positive length three relators.

47 pages including 11 figures. To appear in Journal of Pure and Applied Algebra. Accepted Manuscript