Divisible cube complexes and finite-order automorphisms of RAAGs
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914414889795584 |
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| author | Fioravanti, Elia |
| author_facet | Fioravanti, Elia |
| contents | We give a geometric characterisation of those groups that arise as fixed subgroups of finite-order untwisted automorphisms of right-angled Artin groups (RAAGs). They are precisely the fundamental groups of a class of compact special cube complexes that we term "divisible".
The main corollary is that surface groups arise as fixed subgroups of finite-order automorphisms of RAAGs, as do all commutator subgroups of right-angled Coxeter groups. These appear to be the first examples of such fixed subgroups that are not themselves isomorphic to RAAGs.
Using a variation of canonical completions, we also observe that every special group arises as the fixed subgroup of an automorphism of a finite-index subgroup of a RAAG. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_12680 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Divisible cube complexes and finite-order automorphisms of RAAGs Fioravanti, Elia Group Theory Geometric Topology We give a geometric characterisation of those groups that arise as fixed subgroups of finite-order untwisted automorphisms of right-angled Artin groups (RAAGs). They are precisely the fundamental groups of a class of compact special cube complexes that we term "divisible". The main corollary is that surface groups arise as fixed subgroups of finite-order automorphisms of RAAGs, as do all commutator subgroups of right-angled Coxeter groups. These appear to be the first examples of such fixed subgroups that are not themselves isomorphic to RAAGs. Using a variation of canonical completions, we also observe that every special group arises as the fixed subgroup of an automorphism of a finite-index subgroup of a RAAG. |
| title | Divisible cube complexes and finite-order automorphisms of RAAGs |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2311.12680 |