Automorphisms and subdivisions of Helly graphs
Abstract
We study Helly graphs of finite combinatorial dimension, i.e. whose injective hull is finite-dimensional. We describe very simple fine simplicial subdivisions of the injective hull of a Helly graph, following work of Lang. We also give a very explicit simplicial model of the injective hull of a Helly graphs, in terms of cliques which are intersections of balls. We use these subdivisions to prove that any automorphism of a Helly graph with finite combinatorial dimension is either elliptic or hyperbolic. Moreover, every such hyperbolic automorphism has an axis in an appropriate Helly subdivision, and its translation length is rational with uniformly bounded denominator.
Cite
@article{arxiv.2307.00401,
title = {Automorphisms and subdivisions of Helly graphs},
author = {Thomas Haettel},
journal= {arXiv preprint arXiv:2307.00401},
year = {2023}
}
Comments
This article is a part of the article "Locally elliptic actions, torsion groups, and nonpositively curved spaces" with Damian Osajda, arXiv:2110.12431, which will be split into two parts. v2: final accepted version