Finite groups of untwisted outer automorphisms of RAAGs
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912542205411328 |
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| author | Bregman, Corey Charney, Ruth Vogtmann, Karen |
| author_facet | Bregman, Corey Charney, Ruth Vogtmann, Karen |
| contents | For any right-angled Artin group $A_Γ$, Charney--Stambaugh--Vogtmann showed that the subgroup $U^0(A_Γ) \leq\text{Out}(A_Γ)$ generated by Whitehead automorphisms and inversions acts properly and cocompactly on a contractible space $K_Γ$. In the present paper we show that any finite subgroup of $U^0(A_Γ)$ fixes a point of $K_Γ$. This generalizes the fact that any finite subgroup of $\text{Out}(F_n)$ fixes a point of Outer Space, and implies that there are only finitely many conjugacy classes of finite subgroups in $U^0(A_Γ)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_09222 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finite groups of untwisted outer automorphisms of RAAGs Bregman, Corey Charney, Ruth Vogtmann, Karen Group Theory Geometric Topology 20F65, 20F28, 20F36 For any right-angled Artin group $A_Γ$, Charney--Stambaugh--Vogtmann showed that the subgroup $U^0(A_Γ) \leq\text{Out}(A_Γ)$ generated by Whitehead automorphisms and inversions acts properly and cocompactly on a contractible space $K_Γ$. In the present paper we show that any finite subgroup of $U^0(A_Γ)$ fixes a point of $K_Γ$. This generalizes the fact that any finite subgroup of $\text{Out}(F_n)$ fixes a point of Outer Space, and implies that there are only finitely many conjugacy classes of finite subgroups in $U^0(A_Γ)$. |
| title | Finite groups of untwisted outer automorphisms of RAAGs |
| topic | Group Theory Geometric Topology 20F65, 20F28, 20F36 |
| url | https://arxiv.org/abs/2308.09222 |