Outer Space For 2-Dimensional Raags And Fixed Point Sets Of Finite Subgroups

Abstract

In [CCV07], Charney, Crisp, and Vogtmann construct an outer space for a 2dimensional right-angled Artin group A[GAMMA] . It is a contractible space on which a finite index subgroup Out0 (A[GAMMA] ) of Out(A[GAMMA] ) acts properly. We construct a different outer space S (A[GAMMA] ) for A[GAMMA] and show that non-empty fixed point sets of finite subgroups of Out0 (A[GAMMA] ) 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[GAMMA] ). We present some methods for constructing elements in fixed point sets of finite subgroups and examine cases where such methods are applicable.