Bicombing the mapping class group and Teichm\"uller space via stable cubical intervals
Geometric Topology
2026-01-01 v1 Group Theory
Metric Geometry
Abstract
In this mostly expository article, we provide a new account of our proof with Minsky and Sisto that mapping class groups and Teichm\"uller spaces admit bicombings. More generally, we explain how the hierarchical hull of a pair of points in any colorable hierarchically hyperbolic space is quasi-isometric to a finite CAT(0) cube complex of bounded dimension, with the added property that perturbing the pair of points results in a uniformly bounded change to the cubical structure. Our approach is simplified and new in many aspects.
Cite
@article{arxiv.2512.24136,
title = {Bicombing the mapping class group and Teichm\"uller space via stable cubical intervals},
author = {Matthew Gentry Durham},
journal= {arXiv preprint arXiv:2512.24136},
year = {2026}
}
Comments
57 pages, 9 figures