English

Growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers

Geometric Topology 2019-03-20 v4

Abstract

In this paper we consider the growth rates of 3-dimensional hyperbolic Coxeter polyhedra some of its dihedral angles are πm\frac{\pi}{m} for m7m\geq{7}. By combining with the classical result by Parry \cite{Pa} and the main result of \cite{Y}, we prove that the growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers.

Keywords

Cite

@article{arxiv.1603.04987,
  title  = {Growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers},
  author = {Tomoshige Yukita},
  journal= {arXiv preprint arXiv:1603.04987},
  year   = {2019}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1603.04592; text overlap with arXiv:1504.06718 by other authors