Contractibility of fixed point sets of auter space

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 [J. London Math. Soc. (2) 58 (3) (1998) 633–655]. In more categorical language [Comment. Math. Helv. 73 (1998) 122–136], Xn=EAut(Fn). This is useful because it allows one to compute (see, for example, [7,8]) 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 in [Comment. Math. Helv. 68 (1993) 216–262], who in turn used techniques similar to Culler and Vogtmann in [Invent. Math. 84 (1986) 91–119].