Coxeter systems with $2$-dimensional Davis complexes, growth rates and Perron numbers
Group Theory
2024-07-10 v1 Combinatorics
Geometric Topology
Abstract
In this paper, we study growth rates of Coxeter systems with Davis complexes of dimension at most . We show that if the Euler characteristic of the nerve of a Coxeter system is vanishing (resp. positive), then its growth rate is a Salem (resp. a Pisot) number. In this way, we extend results due to Floyd and Parry. Moreover, in the case where is negative, we provide infinitely many non-hyperbolic Coxeter systems whose growth rates are Perron numbers.
Cite
@article{arxiv.2209.05100,
title = {Coxeter systems with $2$-dimensional Davis complexes, growth rates and Perron numbers},
author = {Naomi Bredon and Tomoshige Yukita},
journal= {arXiv preprint arXiv:2209.05100},
year = {2024}
}