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

✍ Scribed by Craig A. Jensen

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 327 KB
• Volume: 158
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(00)00028-1

✦ Synopsis

For odd primes p, we examine Ĥ * (Aut(F 2(p-1) ); Z (p) ), the Farrell cohomology of the group of automorphisms of a free group F 2(p-1) on 2(P -1) generators, with coe cients in the integers localized at the prime (p) ⊂ Z. This extends results by Glover and Mislin (J. Pure Appl. Algebra 150 (2) (2000)), whose calculations yield Ĥ * (Aut(Fn); Z (p) ) for n ∈ {p -1; p} and is concurrent with work by Chen (Farrell cohomology of automorphism groups of free groups of ÿnite rank, Ohio State University Ph.D. Dissertation, Columbus, Ohio, 1998) 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" (Brown, Cohomology of Groups, Springer, Berlin, 1982), a modiÿcation of Krstic and Vogtmann's (Comment. Math. Helv. 68