Homological stability fails for the Cremona groups
Algebraic Geometry
2024-07-09 v2 Algebraic Topology
Group Theory
Geometric Topology
K-Theory and Homology
Abstract
The Cremona groups are the groups of all birational equivalences of rational varieties and, equivalently, the automorphism groups of the rational function fields. In this note, we explain that homological stability fails for them in both possible ways and comment on their stable homology.
Cite
@article{arxiv.2403.07546,
title = {Homological stability fails for the Cremona groups},
author = {Markus Szymik},
journal= {arXiv preprint arXiv:2403.07546},
year = {2024}
}
Comments
6 pages