Nielsen realisation for untwisted automorphisms of right-angled Artin groups

Abstract

We prove Nielsen realisation for finite subgroups of the groups of untwisted outer automorphisms of RAAGs in the following sense: given any graph $\Gamma$, and any finite group $G⩽{\mathrm{U}}^0(A_{\Gamma })⩽{\mathrm{Out}}^0(A_{\Gamma })$, we find a non-positively curved cube complex with fundamental group $A_{\Gamma }$ on which $G$ acts by isometries, realising the action on $A_{\Gamma }$.

60 pages, 3 figures; major rewrite. Extended results to all dimensions. The relative Nielsen realisation for free groups proved in the previous version is now contained in a separate paper (arXiv:1601.02187)

References in corpus (3)

• Outer space for untwisted automorphisms of right-angled Artin groups
• Realisation and dismantlability
• Nielsen Realisation by Gluing: Limit Groups and Free Products

Cited by in corpus (6)

• Relative automorphism groups of right-angled Artin groups
• Coarse-median preserving automorphisms
• On automorphisms and splittings of special groups
• Right-angled Artin groups as finite-index subgroups of their outer automorphism groups
• Finite groups of untwisted outer automorphisms of RAAGs
• Divisible cube complexes and finite-order automorphisms of RAAGs