Coxeter systems with $2$-dimensional Davis complexes, growth rates and Perron numbers
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913422049804288 |
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| author | Bredon, Naomi Yukita, Tomoshige |
| author_facet | Bredon, Naomi Yukita, Tomoshige |
| contents | In this paper, we study growth rates of Coxeter systems with Davis complexes of dimension at most $2$. We show that if the Euler characteristic $χ$ of the nerve of a Coxeter system is vanishing (resp. positive), then its growth rate is a Salem (resp. a Pisot) number. In this way, we extend results due to Floyd and Parry. Moreover, in the case where $χ$ is negative, we provide infinitely many non-hyperbolic Coxeter systems whose growth rates are Perron numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05100 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Coxeter systems with $2$-dimensional Davis complexes, growth rates and Perron numbers Bredon, Naomi Yukita, Tomoshige Group Theory Combinatorics Geometric Topology 20F55 (Primary) 20F65 (Secondary) In this paper, we study growth rates of Coxeter systems with Davis complexes of dimension at most $2$. We show that if the Euler characteristic $χ$ of the nerve of a Coxeter system is vanishing (resp. positive), then its growth rate is a Salem (resp. a Pisot) number. In this way, we extend results due to Floyd and Parry. Moreover, in the case where $χ$ is negative, we provide infinitely many non-hyperbolic Coxeter systems whose growth rates are Perron numbers. |
| title | Coxeter systems with $2$-dimensional Davis complexes, growth rates and Perron numbers |
| topic | Group Theory Combinatorics Geometric Topology 20F55 (Primary) 20F65 (Secondary) |
| url | https://arxiv.org/abs/2209.05100 |