(Non-)Vanishing of high-dimensional group cohomology

TL;DR

This survey reviews the current progress on stability and vanishing conjectures in high-dimensional cohomology for groups like SL_n(Z), surface mapping class groups, and automorphism groups of free groups.

Contribution

It summarizes the latest developments and generalizations related to the stability and vanishing conjectures in high-dimensional group cohomology.

Findings

Summary of recent progress on conjectures

Identification of open problems and directions

Overview of generalizations and related results

Abstract

Church-Farb-Putman formulated stability and vanishing conjectures for the high-dimensional cohomology of $\operatorname{SL}_n(\mathbb{Z})$, surface mapping class groups and automorphism groups of free groups. This is a survey on the current status of these conjectures and their generalisations.