English

Mapping class groups are quasicubical

Metric Geometry 2024-07-02 v3 Group Theory

Abstract

It is proved that the mapping class group of any closed surface with finitely many marked points is quasiisometric to a CAT(0) cube complex. We provide two distinct proofs, one tailored to mapping class groups, and one applying to a larger class of groups.

Keywords

Cite

@article{arxiv.2112.10681,
  title  = {Mapping class groups are quasicubical},
  author = {Harry Petyt},
  journal= {arXiv preprint arXiv:2112.10681},
  year   = {2024}
}

Comments

28 pages. v3: Accepted version. v2: Improved exposition

R2 v1 2026-06-24T08:24:54.514Z