Deciding if a hyperbolic group splits over a given quasiconvex subgroup
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866913365968814080 |
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| author | MacManus, Joseph |
| author_facet | MacManus, Joseph |
| contents | We present an algorithm which decides whether a given quasiconvex residually finite subgroup $H$ of a hyperbolic group $G$ is associated with a splitting. The methods developed also provide algorithms for computing the number of filtered ends $\tilde e(G,H)$ of $H$ in $G$ under certain hypotheses, and give a new straightforward algorithm for computing the number of ends $e(G,H)$ of the Schreier graph of $H$. Our techniques extend those of Barrett via the use of labelled digraphs, the languages of which encode information on the connectivity of $\partial G - ΛH$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_09973 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Deciding if a hyperbolic group splits over a given quasiconvex subgroup MacManus, Joseph Group Theory 20F67, 20F65, 20F10 We present an algorithm which decides whether a given quasiconvex residually finite subgroup $H$ of a hyperbolic group $G$ is associated with a splitting. The methods developed also provide algorithms for computing the number of filtered ends $\tilde e(G,H)$ of $H$ in $G$ under certain hypotheses, and give a new straightforward algorithm for computing the number of ends $e(G,H)$ of the Schreier graph of $H$. Our techniques extend those of Barrett via the use of labelled digraphs, the languages of which encode information on the connectivity of $\partial G - ΛH$. |
| title | Deciding if a hyperbolic group splits over a given quasiconvex subgroup |
| topic | Group Theory 20F67, 20F65, 20F10 |
| url | https://arxiv.org/abs/2210.09973 |