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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2112.09440 |
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| _version_ | 1866914822182928384 |
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| author | Tselekidis, Panagiotis |
| author_facet | Tselekidis, Panagiotis |
| contents | Let $W_Γ$ be the Right-Angled Coxeter group with defining graph $Γ$. We show that the asymptotic dimension of $W_Γ$ is smaller than or equal to $dim_{CC}(Γ)$, the clique-connected dimension of the graph. As a corollary we show that $W_Γ$ is virtually free if and only if $dim_{CC}(Γ)=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_09440 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A new upper bound for the Asymptotic Dimension of RACGs Tselekidis, Panagiotis Group Theory Let $W_Γ$ be the Right-Angled Coxeter group with defining graph $Γ$. We show that the asymptotic dimension of $W_Γ$ is smaller than or equal to $dim_{CC}(Γ)$, the clique-connected dimension of the graph. As a corollary we show that $W_Γ$ is virtually free if and only if $dim_{CC}(Γ)=1$. |
| title | A new upper bound for the Asymptotic Dimension of RACGs |
| topic | Group Theory |
| url | https://arxiv.org/abs/2112.09440 |