Braiding groups of automorphisms and almost-automorphisms of trees
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866916237912571904 |
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| author | Skipper, Rachel Zaremsky, Matthew C. B. |
| author_facet | Skipper, Rachel Zaremsky, Matthew C. B. |
| contents | We introduce "braided" versions of self-similar groups and Röver--Nekrashevych groups, and study their finiteness properties. This generalizes work of Aroca and Cumplido, and the first author and Wu, who considered the case when the self-similar groups are what we call "self-identical". In particular we use a braided version of the Grigorchuk group to construct a new group called the braided Röver group, which we prove is of type $F_\infty$. Our techniques involve using so called $d$-ary cloning systems to construct the groups, and analyzing certain complexes of embedded disks in a surface to understand their finiteness properties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2109_13389 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Braiding groups of automorphisms and almost-automorphisms of trees Skipper, Rachel Zaremsky, Matthew C. B. Group Theory Geometric Topology Primary 20F65, Secondary 57M07 We introduce "braided" versions of self-similar groups and Röver--Nekrashevych groups, and study their finiteness properties. This generalizes work of Aroca and Cumplido, and the first author and Wu, who considered the case when the self-similar groups are what we call "self-identical". In particular we use a braided version of the Grigorchuk group to construct a new group called the braided Röver group, which we prove is of type $F_\infty$. Our techniques involve using so called $d$-ary cloning systems to construct the groups, and analyzing certain complexes of embedded disks in a surface to understand their finiteness properties. |
| title | Braiding groups of automorphisms and almost-automorphisms of trees |
| topic | Group Theory Geometric Topology Primary 20F65, Secondary 57M07 |
| url | https://arxiv.org/abs/2109.13389 |