On the growth rate of ideal Coxeter groups in hyperbolic 3-space

Yohei Komori; Tomoshige Yukita

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arXiv · 1507.02481

On the growth rate of ideal Coxeter groups in hyperbolic 3-space

Yohei Komori·Tomoshige Yukita

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Abstract

We study the set G of growth rates of of ideal Coxeter groups in hyperbolic 3-space which consists of real algebraic integers greater than 1. We show that (1) G is unbounded above while it has the minimum, (2) any element of G is a Perron number, and (3) growth rates of of ideal Coxeter groups with $n$ generators are located in the closed interval $[n-3, n-1]$.

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Yohei Komori, Tomoshige Yukita. 2015-07-09. On the growth rate of ideal Coxeter groups in hyperbolic 3-space. https://arxiv.org/abs/1507.02481

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