First PositionKnowledge engineering at Reasoning Mind
DissertationOuter Space for Two-Dimensional RAAGs and Fixed Point Sets of Finite Subgroups
In [CCV07], Charney, Crisp, and Vogtmann construct an outer space for a 2-dimensional right-angled Artin group AΓ. It is a contractible space on which a finite index subgroup Out0(AΓ) of Out(AΓ) acts properly. We construct a different outer space S(AΓ) for AΓ and show that non-empty fixed point sets of finite subgroups of Out0(AΓ) 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(AΓ). We present some methods for constructing elements in fixed point sets of finite subgroups and examine cases where such methods are applicable.