The stable cohomology of automorphisms of free groups with coefficients in the homology representation

Details The stable cohomology of automorphisms of free groups with coefficients in the homology representation The stable cohomology of automorphisms of free groups with coefficients in the homology representation

2010-12-07

arxiv.org/abs/1012.1433v1

Mathematics

Algebraic Topology

Scientific paper

We study the cohomology of Aut(F_n) and Out(F_n) with coefficients in the modules \wedge^q H, \wedge H^*, Sym^q H or Sym^q H^*, where H is the Out(F_n)-module obtained by abelianising the free group F_n. For reasons which are not conceptually clear, taking coefficients in H and its related modules behaves in a far less trivial way than taking coefficients in H^* and its related modules. Based on a conjectural homology stability theorem for spaces of graphs labeled by a simply connected background space, we give a stable integral calculation of these groups in low degrees, and modulo a further conjecture a stable rational calculation in all degrees.

Affiliated with

Also associated with

No associations

Rating

The stable cohomology of automorphisms of free groups with coefficients in the homology representation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The stable cohomology of automorphisms of free groups with coefficients in the homology representation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The stable cohomology of automorphisms of free groups with coefficients in the homology representation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-479793