Mapping class groups are quasicubical

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

Authors

Publication Details

Journal
American Journal of Mathematics
Published
2026-05-30
DOI
https://doi.org/10.1353/ajm.2026.a991628
Citations
2
Primary Topic
Geometric and Algebraic Topology
Type
preprint
Field-Weighted Citation Impact
0.00
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preprint

Mapping class groups are quasicubical

Harry Petyt
2 citations
American Journal of Mathematics
Geometric and Algebraic Topology
preprint

Mapping class groups are quasicubical

Harry Petyt
preprint en
2 citations

Abstract

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

American Journal of MathematicsVol. 148(3)
Openalex Percentile: Top 99%
Geometric and Algebraic Topology
DOIOpen Access PDFOpenAlex
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