Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866912759903420416 |
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| author | Kellerhals, Ruth Liechti, Livio |
| author_facet | Kellerhals, Ruth Liechti, Livio |
| contents | We show that not every Salem number appears as the growth rate of a cocompact hyperbolic Coxeter group. We also give a new proof of the fact that the growth rates of planar hyperbolic Coxeter groups are spectral radii of Coxeter transformations, and show that this need not be the case for growth rates of hyperbolic tetrahedral Coxeter groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_10965 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups Kellerhals, Ruth Liechti, Livio Group Theory Geometric Topology Number Theory 20F55, 11R06, 22E40, 11K16 We show that not every Salem number appears as the growth rate of a cocompact hyperbolic Coxeter group. We also give a new proof of the fact that the growth rates of planar hyperbolic Coxeter groups are spectral radii of Coxeter transformations, and show that this need not be the case for growth rates of hyperbolic tetrahedral Coxeter groups. |
| title | Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups |
| topic | Group Theory Geometric Topology Number Theory 20F55, 11R06, 22E40, 11K16 |
| url | https://arxiv.org/abs/2008.10965 |