Abstract :
For odd primes p, we examine image, 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 image. This extends results by Glover and Mislin (J. Pure Appl. Algebra 150 (2) (2000)), whose calculations yield image for nset membership, variant{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 image for nset membership, variant{p+1,p+2}. The main tools used are Ken Brownʹs “normalizer spectral sequence” (Brown, Cohomology of Groups, Springer, Berlin, 1982), a modification of Krstic and Vogtmannʹs (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. Soc. (2) 58 (3)(1998) 633–655).
