Contractibility of fixed point sets of auter space

الأصل · EN

We show that for every finite subgroup G of Aut(Fₙ), the fixed point subcomplex Xₙᵍ is contractible, where Fₙ is the free group on n letters and Xₙ is the spine of ``auter space'' constructed by Hatcher and Vogtmann. In more categorical language, Xₙ =EAut(Fₙ). This is useful because it allows one to compute the cohomology of normalizers or centralizers of finite subgroups of Aut(Fₙ) based on their actions on fixed point subcomplexes. The techniques used to prove it are largely those of Krstic and Vogtmann, who in turn used techniques similar to Culler and Vogtmann.