A note on almost negative matrices and Gromov-hyperbolic Coxeter groups

Abstract

In this note we revisit Moussong's Characterization of Gromov-hyperbolic Coxeter groups. A Coxeter group is Gromov-hyperbolic if and only if it does not contain a subgroup isomorphic to $\mathbb{Z}^2$ which can be read off directly from the defining graph. We show that there is a small gap in the original argument and provide a workaround.