(Non-)Vanishing of high-dimensional group cohomology

Benjamin Brück

(Non-)Vanishing of high-dimensional group cohomology

Group Theory 2025-10-13 v4 Algebraic Topology Number Theory

Authors: Benjamin Brück

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.

Keywords

group cohomology stability conjectures vanishing conjectures SL_n(Z) mapping class groups

Cite

@article{arxiv.2404.15026,
  title  = {(Non-)Vanishing of high-dimensional group cohomology},
  author = {Benjamin Brück},
  journal= {arXiv preprint arXiv:2404.15026},
  year   = {2025}
}

Comments

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

(Non-)Vanishing of high-dimensional group cohomology

Abstract

Keywords

Cite

Comments

Related papers