Relative Untwisted Outer Space for Right-Angled Artin Groups
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916650967629824 |
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| author | Abgrall, Adrien |
| author_facet | Abgrall, Adrien |
| contents | For G, H two finite collections of finitely generated subgroups of a right-angled Artin group A, the untwisted McCool group U(A; G, Ht) is the subgroup of untwisted outer automorphisms of A preserving the conjugacy class of each element of G and acting trivially up to conjugacy on each element of H. We prove that when the elements of G are standard subgroups of A, U(A; G, Ht) acts properly cocompactly on a finite-dimensional subcomplex of the spine of untwisted outer space for A, providing a geometric model for this group and proof that it is of type VF. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09588 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relative Untwisted Outer Space for Right-Angled Artin Groups Abgrall, Adrien Group Theory Geometric Topology 20F28 (Primary) 20F36, 20F65 (Secondary) For G, H two finite collections of finitely generated subgroups of a right-angled Artin group A, the untwisted McCool group U(A; G, Ht) is the subgroup of untwisted outer automorphisms of A preserving the conjugacy class of each element of G and acting trivially up to conjugacy on each element of H. We prove that when the elements of G are standard subgroups of A, U(A; G, Ht) acts properly cocompactly on a finite-dimensional subcomplex of the spine of untwisted outer space for A, providing a geometric model for this group and proof that it is of type VF. |
| title | Relative Untwisted Outer Space for Right-Angled Artin Groups |
| topic | Group Theory Geometric Topology 20F28 (Primary) 20F36, 20F65 (Secondary) |
| url | https://arxiv.org/abs/2503.09588 |