Oscar Randal-Williams
Published 2010-12-07Version 1
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.
First cohomology groups of the automorphism group of a free group with coefficients in the abelianization of the IA-automorphism group
On the stable cohomology of $\mathrm{GL}(n, \mathbb{Z})$, $\mathrm{Aut}(F_n)$ and $\mathrm{IA}_n$
The walled Brauer category and stable cohomology of $\mathrm{IA}_n$
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