Stable cubulations, bicombings, and barycenters
Group Theory
2023-09-06 v1 Geometric Topology
Metric Geometry
Abstract
We prove that the hierarchical hulls of finite sets of points in mapping class groups and Teichm\"uller spaces are stably approximated by a CAT(0) cube complexes, strengthening a result of Behrstock-Hagen-Sisto. As applications, we prove that mapping class groups are semihyperbolic and Teichm\"uller spaces are coarsely equivariantly bicombable, and both admit stable coarse barycenters. Our results apply to the broader class of "colorable" hierarchically hyperbolic spaces and groups.
Keywords
Cite
@article{arxiv.2009.13647,
title = {Stable cubulations, bicombings, and barycenters},
author = {Matthew G. Durham and Yair N. Minsky and Alessandro Sisto},
journal= {arXiv preprint arXiv:2009.13647},
year = {2023}
}
Comments
80 pages, 25 figures