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arXiv · 1306.3443

Growth rates of cocompact hyperbolic Coxeter groups and 2-Salem numbers

Yuriko Umemoto
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Abstract

By the results of Cannon, Wagreich and Parry, it is known that the growth rate of a cocompact Coxeter group in 2-dimensional hyperbolic space $H^2$ and 3-dimensional hyperbolic space $H^3$ is a Salem number. Kerada defined a j-Salem number, which is a generalization of a Salem number. In this paper, we realize infinitely many 2-Salem numbers as the growth rates of cocompact Coxeter groups in 4-dimensional hyperbolic space $H ^4$. Our Coxeter polytopes are constructed by successive gluing of Coxeter polytopes which we call Coxeter dominoes.

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Yuriko Umemoto. 2013-06-14. Growth rates of cocompact hyperbolic Coxeter groups and 2-Salem numbers. https://doi.org/10.2140/agt.2014.14.2721

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