On the mod-p cohomology of Out(F2(p−1

Abstract

Communicated by E.M. Friedlander MSC: Primary: 20J06 Secondary: 20F28; 20F65; 55N91 a b s t r a c tWe 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 precisely, 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 ≤ 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 ).