Finite conjugacy classes and split exact cochain complexes
Group Theory
2022-06-09 v1 Functional Analysis
Abstract
We study the cohomology of isometric group actions on (super) reflexive Banach spaces with a focus on the relation between finite conjugacy classes and split exactness of cochain complexes. In particular, we show that, if a uniformly convex Banach module has no almost invariant vectors under the FC-centre of the acting group, then the associated cochain complex is split exact. Other similar rigidity results are established that are related to prior work of Bader - Furman - Gelander - Monod, Bader - Rosendal - Sauer and Nowak.
Keywords
Cite
@article{arxiv.2206.03558,
title = {Finite conjugacy classes and split exact cochain complexes},
author = {Christian Rosendal},
journal= {arXiv preprint arXiv:2206.03558},
year = {2022}
}