Geometry for palindromic automorphism groups of free groups

We examine the palindromic automorphism group ΠA(Fn) of a free group Fn, a group first defined by Collins in [5] which is related to hyperelliptic involutions of mapping class groups, congruence subgroups of SLn(Z), and symmetric automorphism groups of free groups. Cohomological properties of the group are explored by looking at a contractible space on which ΠA(Fn) acts properly with finite quotient. Our results answer some conjectures of Collins and provide a few striking results about the cohomology of ΠA(Fn), such as that its rational cohomology is zero at the vcd. AMS Classification 20F32, 20J05; 20F28, 55N91