2 00 1 Cohomology of Aut ( F n ) in the p - rank two case

For odd primes p, we examine Ĥ(Aut(F2(p−1));Z(p)), the Farrell cohomology of the group of automorphisms of a free group F2(p−1) on 2(p − 1) generators, with coefficients in the integers localized at the prime (p) ⊂ Z. This extends results in [9] by Glover and Mislin, whose calculations yield Ĥ(Aut(Fn);Z(p)) for n ∈ {p− 1, p} and is concurrent with work by Chen in [6] where he calculates Ĥ(Aut(Fn);Z(p)) for n ∈ {p+1, p+2}. The main tools used are Ken Brown’s “normalizer spectral sequence” from [4], a modification of Krstic and Vogtmann’s proof of the contractibility of fixed point sets for outer space in [16], and a modification of the Degree Theorem of Hatcher and Vogtmann in [11].