The growth function of Coxeter dominoes and 2–Salem numbers

Umemoto, Yuriko¹

¹Department of Mathematics, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

Algebraic and Geometric Topology, Tome 14 (2014) no. 5, pp. 2721-2746

Résumé

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.

Détail

DOI : 10.2140/agt.2014.14.2721

Classification : 20F55, 20F65, 11K16
Keywords: hyperbolic Coxeter group, growth rate, $2$–Salem number

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