Geometry for palindromic automorphism groups of free groups

Abstract

We examine the palindromic automorphism group A(Fn) of a free group Fn, a group first defined by Collins in Cohomological properties of the group are explored by looking at a contractible space on which A(Fn) acts properly with finite quotient. Our results answer some conjectures of Collins and provide a few striking results about the cohomology of A(Fn), such as that its rational cohomology is zero at the vcd.