(Non-)Vanishing of high-dimensional group cohomology

Abstract

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

18 pages, 5 figures; contribution to the proceedings of the conference Model theory and groups 2023; v2: updated references and corrected typos; v3: revision after referee report; v4: corrected a mistake in Figure 1