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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

R2 v1 2026-06-28T15:17:06.819Z