Centralisers of linear growth automorphisms of free groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912150069444608 |
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| author | Andrew, Naomi Martino, Armando |
| author_facet | Andrew, Naomi Martino, Armando |
| contents | In this note we investigate the centraliser of a linearly growing element of $\mathrm{Out}(F_n)$ (that is, a root of a Dehn twist automorphism), and show that it has a finite index subgroup mapping onto a direct product of certain "equivariant McCool groups" with kernel a finitely generated free abelian group. In particular, this allows us to show it is VF and hence finitely presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_12865 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Centralisers of linear growth automorphisms of free groups Andrew, Naomi Martino, Armando Group Theory 20E36 (Primary) 20E05, 20E08 (Secondary) In this note we investigate the centraliser of a linearly growing element of $\mathrm{Out}(F_n)$ (that is, a root of a Dehn twist automorphism), and show that it has a finite index subgroup mapping onto a direct product of certain "equivariant McCool groups" with kernel a finitely generated free abelian group. In particular, this allows us to show it is VF and hence finitely presented. |
| title | Centralisers of linear growth automorphisms of free groups |
| topic | Group Theory 20E36 (Primary) 20E05, 20E08 (Secondary) |
| url | https://arxiv.org/abs/2205.12865 |