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

Philip Möller

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

Group Theory 2023-09-20 v2

Authors: Philip Möller

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.

Keywords

hyperbolic groups coxeter groups

Cite

@article{arxiv.2205.07791,
  title  = {A note on almost negative matrices and Gromov-hyperbolic Coxeter groups},
  author = {Philip Möller},
  journal= {arXiv preprint arXiv:2205.07791},
  year   = {2023}
}

Comments

V2: Fixed Typoes and provided additional arguments to fix an additional problem with the original. 19 Pages, 5 Figures. Comments are welcome!

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