Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers

Details Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers

2011-05-31

arxiv.org/abs/1105.6267v5

Mathematics

Metric Geometry

26 pages, 16 figures, 4 data tables; minor corrections; European Journal of Combinatorics, 2012

Scientific paper

A connection between real poles of the growth functions for Coxeter groups acting on hyperbolic space of dimensions three and greater and algebraic integers is investigated. In particular, a geometric convergence of fundamental domains for cocompact hyperbolic Coxeter groups with finite-volume limiting polyhedron provides a relation between Salem numbers and Pisot numbers. Several examples conclude this work.

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