Cohomology of Aut(Fn) in the p-rank two case

For odd primes p, we examine H*(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)subset of Z. This extends results by Glover and Mislin (J. Pure Appl. Algebra 150 (2) (2000)), whose calculations yield H*(Aut(F-n); Z((p))) for n is an element of (p - 1. p) and is concurrent with work by Chen (Farrell cohomology of automorphism groups of free groups of finite rank, Ohio State University Ph.D. Dissertation, Columbus, Ohio, 1998) where he calculates H*(Aut(F-n); Z((p))) for n is an element of (p + 1, p + 2). The main tools used are Ken Brown's "normalizer spectral sequence" (Brown, Cohomology of Groups, Springer, Berlin, 1982), a modification of Krstic and Vogtmanns (Comment. Math. Helv. 68 (1993) 216-262) proof of the contractibility of fixed point sets for outer space. and a modification of the Degree Theorem of Hatcher and Vogtmann (J. London Math. Sec. (2) 58 (3)(1998) 633-655). (C) 2001 Elsevier Science B.V. All rights reserved.