## Algebraic & Geometric Topology

### The growth function of Coxeter dominoes and $2$–Salem numbers

Yuriko Umemoto

#### Abstract

By the results of Cannon, Wagreich and Parry, it is known that the growth rate of a cocompact Coxeter group in $ℍ2$ and $ℍ3$ is a Salem number. Kerada defined a $j$–Salem number, which is a generalization of Salem numbers. In this paper, we realize infinitely many $2$–Salem numbers as the growth rates of cocompact Coxeter groups in $ℍ4$. Our Coxeter polytopes are constructed by successive gluing of Coxeter polytopes, which we call Coxeter dominoes.

#### Article information

Source
Algebr. Geom. Topol., Volume 14, Number 5 (2014), 2721-2746.

Dates
Revised: 4 September 2013
Accepted: 10 September 2013
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513716001

Digital Object Identifier
doi:10.2140/agt.2014.14.2721

Mathematical Reviews number (MathSciNet)
MR3276846

Zentralblatt MATH identifier
1307.20036

#### Citation

Umemoto, Yuriko. The growth function of Coxeter dominoes and $2$–Salem numbers. Algebr. Geom. Topol. 14 (2014), no. 5, 2721--2746. doi:10.2140/agt.2014.14.2721. https://projecteuclid.org/euclid.agt/1513716001

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