Stable cohomology of $Aut(F_n)$ with bivariant twisted coefficients

TL;DR

This paper calculates the cohomology groups of automorphism groups of free groups with complex twisted coefficients, revealing new algebraic structures in a specific stable range.

Contribution

It provides the first comprehensive computation of these cohomology groups with tensor product coefficients for large n, extending known results.

Findings

Cohomology groups computed for large n

Results apply to tensor products of standard and dual representations

New algebraic structures identified in automorphism groups

Abstract

We compute the cohomology groups of the automorphism group of the free group $F_n$, with coefficients in arbitrary tensor products of the standard representation $H_1(F_n, \mathbb{Q})$ and its dual, in a range where $n$ is sufficiently large compared to the cohomological degree and the number of tensor factors.