Victor Kostyuk

In [CCV07], Charney, Crisp, and Vogtmann construct an outer space for a 2-dimensional right-angled Artin group A_Γ. It is a contractible space on which a finite index subgroup Out⁰(A_Γ) of Out(A_Γ) acts properly. We construct a different outer space S(A_Γ) for A_Γ and show that non-empty fixed point sets of finite subgroups of Out⁰(A_Γ) are contractible in this space. While Culler’s realization theorem ([Cul84]) implies that fixed point sets of finite subgroups of Out(Fn) are always non-empty in the Culler-Vogtmann outer space, there is no direct counterpart to this result in the case of right-angled Artin groups and S(A_Γ). We present some methods for constructing elements in fixed point sets of finite subgroups and examine cases where such methods are applicable.