On the mod - p cohomology of Out(F_{2(p-1)}

Henry Glover (1) , Hans-Werner Henn (2)

1 Department of Mathematics
2 IRMA - Institut de Recherche Mathématique Avancée

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).

Domaines: Topologie algébrique [math.AT]

Henry Glover, Hans-Werner Henn. On the mod - p cohomology of Out(F_{2(p-1)}. Journal of Pure and Applied Algebra, 2010. ⟨hal-00336128⟩