A stability conjecture for the unstable cohomology of SL_n Z, mapping class groups, and Aut(F_n)

TL;DR

This paper proposes a conjecture regarding the stability and vanishing of significant parts of the unstable rational cohomology in groups like SL_n Z, mapping class groups, and Aut(F_n), aiming to unify understanding across these areas.

Contribution

It introduces a conjecture suggesting stability and vanishing patterns in the unstable rational cohomology of key algebraic and geometric groups.

Findings

Conjecture on stability and vanishing of unstable cohomology.

Potential implications for understanding group cohomology.

Framework for future proofs and research directions.

Abstract

In this paper we conjecture the stability and vanishing of a large piece of the unstable rational cohomology of SL_n Z, of mapping class groups, and of Aut(F_n).