Visual right-angled Artin subgroups of two-dimensional right-angled Coxeter groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918194707431424 |
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| author | Cashen, Christopher H. Edletzberger, Alexandra |
| author_facet | Cashen, Christopher H. Edletzberger, Alexandra |
| contents | There is a procedure, due to Dani and Levcovitz, for taking a finite simplicial graph (Γ) and a subgraph (Λ) of its complement, checking some conditions, and, if satisfied, producing a graph (Δ) such that the right-angled Artin group with presentation graph (Δ) is a finite index subgroup of the right-angled Coxeter group with presentation graph (Γ). They do not tell us how to find (Λ), given (Γ).
We show, in the 2--dimensional case, that the existence of such a (Λ) is connected to the graph property of satellite-dismantlabilty of (Γ), and we use this to give an algorithm for producing a suitable (Λ) or deciding that one does not exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04817 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Visual right-angled Artin subgroups of two-dimensional right-angled Coxeter groups Cashen, Christopher H. Edletzberger, Alexandra Group Theory 20F65, 20F55 There is a procedure, due to Dani and Levcovitz, for taking a finite simplicial graph (Γ) and a subgraph (Λ) of its complement, checking some conditions, and, if satisfied, producing a graph (Δ) such that the right-angled Artin group with presentation graph (Δ) is a finite index subgroup of the right-angled Coxeter group with presentation graph (Γ). They do not tell us how to find (Λ), given (Γ). We show, in the 2--dimensional case, that the existence of such a (Λ) is connected to the graph property of satellite-dismantlabilty of (Γ), and we use this to give an algorithm for producing a suitable (Λ) or deciding that one does not exist. |
| title | Visual right-angled Artin subgroups of two-dimensional right-angled Coxeter groups |
| topic | Group Theory 20F65, 20F55 |
| url | https://arxiv.org/abs/2405.04817 |