Growth rates of cocompact hyperbolic Coxeter groups and 2-Salem numbers

Abstract

By the results of Cannon, Wagreich and Parry, it is known that the growth rate of a cocompact Coxeter group in 2-dimensional hyperbolic space $H^2$ and 3-dimensional hyperbolic space $H^3$ is a Salem number. Kerada defined a j-Salem number, which is a generalization of a Salem number. In this paper, we realize infinitely many 2-Salem numbers as the growth rates of cocompact Coxeter groups in 4-dimensional hyperbolic space $H^4$. Our Coxeter polytopes are constructed by successive gluing of Coxeter polytopes which we call Coxeter dominoes.

21 pages, 12 figures

Cited by in corpus (4)

• Survey article: Seventy years of Salem numbers
• A Proof of the Conjecture of Lehmer and of the Conjecture of Schinzel-Zassenhaus
• Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups
• Construction of infinite series of non-simple ideal hyperbolic Coxeter 4-polytopes and their growth rates