Algebraic & Geometric Topology

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

Yuriko Umemoto

Full-text: Open access

Abstract

By the results of Cannon, Wagreich and Parry, it is known that the growth rate of a cocompact Coxeter group in 2 and 3 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 4. 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
Received: 20 May 2013
Revised: 4 September 2013
Accepted: 10 September 2013
First available in Project Euclid: 19 December 2017

Permanent link to this document
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

Subjects
Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 11K16: Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63]

Keywords
hyperbolic Coxeter group growth rate $2$–Salem number

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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