Ttitle:
On the mod-p cohomology of Out(F_{2(p-1)})
Authors:
Henry Glover
glover@math.ohio-state.edu
Hans-Werner Henn
henn@math.u-strasbg.fr
Abstract:
We study the mod-p cohomology of the group Out(F_n)
of outer automorphisms of the free group F_n
in the case n=2(p-1) which is the smallest n for which the
p-rank of this group is 2. For p=3 we give a complete computation,
at least above the virtual cohomological dimension of Out(F_4)
(which is 5). More precisley, we calculate the equivariant
cohomology of the p-singular part of outer space for p=3.
For a general prime p>3 we give a recursive description in terms of
the mod-p cohomology of Aut(F_k) for k less or equal to p-1.
In this case we use the Out(F_{2(p-1)})-equivariant cohomology
of the poset of elementary abelian p-subgroups of Out(F_n).