Volume 14, issue 5 (2014)

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

Yuriko Umemoto

Algebraic & Geometric Topology 14 (2014) 2721–2746
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.

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