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 $Γ$, and any finite group $G\leqslant \mathrm{U}^0(A_Γ) \leqslant \mathrm{Out}^0(A_Γ)$, we find a non-positively curved cube complex with fundamental group $A_Γ$ on which $G$ acts by isometries, realising the action on $A_Γ$.

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)