On finite presentability of some partial Torelli subgroups of Aut(F_n)
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917183172378624 |
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| author | Ershov, Mikhail |
| author_facet | Ershov, Mikhail |
| contents | Let $F_n$ be the free group of rank $n$, and let $ρ_{ab}:\mathrm{Aut}(F_n)\to \mathrm{GL}_n(\mathbb Z)$ be the map induced by the natural projection $F_n\to\mathbb Z^n$. It is a long-standing open problem whether the subgroup of $\mathrm{IA}$-automorphisms $\mathrm{IA}_n=\mathrm{Ker}ρ_{ab}$ is finitely presented for $n\geq 4$. In this paper we establish finite presentability of certain infinite index subgroups of $\mathrm{Aut}(F_n)$ containing $\mathrm{IA}_n$. In the terminology of Putman, these subgroups are natural analogues of partial Torelli subgroups of mapping class groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01377 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On finite presentability of some partial Torelli subgroups of Aut(F_n) Ershov, Mikhail Group Theory Primary 20F05, 20F65, Secondary 20F06, 20F28, 57M07 Let $F_n$ be the free group of rank $n$, and let $ρ_{ab}:\mathrm{Aut}(F_n)\to \mathrm{GL}_n(\mathbb Z)$ be the map induced by the natural projection $F_n\to\mathbb Z^n$. It is a long-standing open problem whether the subgroup of $\mathrm{IA}$-automorphisms $\mathrm{IA}_n=\mathrm{Ker}ρ_{ab}$ is finitely presented for $n\geq 4$. In this paper we establish finite presentability of certain infinite index subgroups of $\mathrm{Aut}(F_n)$ containing $\mathrm{IA}_n$. In the terminology of Putman, these subgroups are natural analogues of partial Torelli subgroups of mapping class groups. |
| title | On finite presentability of some partial Torelli subgroups of Aut(F_n) |
| topic | Group Theory Primary 20F05, 20F65, Secondary 20F06, 20F28, 57M07 |
| url | https://arxiv.org/abs/2601.01377 |