The growth function of Coxeter dominoes and 2–Salem numbers

Umemoto, Yuriko

doi:10.2140/agt.2014.14.2721

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

Yuriko Umemoto

Algebraic & Geometric Topology 14 (2014) 2721–2746

DOI: 10.2140/agt.2014.14.2721

Abstract

By the results of Cannon, Wagreich and Parry, it is known that the growth rate of a cocompact Coxeter group in $ℍ^{2}$ and $ℍ^{3}$ 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 $ℍ^{4}$ . Our Coxeter polytopes are constructed by successive gluing of Coxeter polytopes, which we call Coxeter dominoes.

Keywords

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

Mathematical Subject Classification 2010

Primary: 20F55

Secondary: 20F65, 11K16

References

Publication

Received: 20 May 2013

Revised: 4 September 2013

Accepted: 10 September 2013

Published: 5 November 2014

Authors

Yuriko Umemoto
Department of Mathematics Osaka City University 3-3-138, Sugimoto, Sumiyoshi-ku Osaka 558-8585 Japan

Volume 14, issue 5 (2014)