TY - JOUR
T1 - Stable cubulations, bicombings, and barycenters
AU - Durham, Matthew Gentry
AU - Minsky, Yair N.
AU - Sisto, Alessandro
PY - 2023/8/25
Y1 - 2023/8/25
N2 - We prove that the hierarchical hulls of finite sets of points in mapping class groups and Teichmüller spaces are stably approximated by CAT(0) cube complexes, strengthening a result of Behrstock, Hagen and Sisto. As applications, we prove that mapping class groups are semihyperbolic and Teichmüller 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.
AB - We prove that the hierarchical hulls of finite sets of points in mapping class groups and Teichmüller spaces are stably approximated by CAT(0) cube complexes, strengthening a result of Behrstock, Hagen and Sisto. As applications, we prove that mapping class groups are semihyperbolic and Teichmüller 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.
UR - http://www.scopus.com/inward/record.url?scp=85170535444&partnerID=8YFLogxK
U2 - 10.2140/gt.2023.27.2383
DO - 10.2140/gt.2023.27.2383
M3 - Article
SN - 1465-3060
VL - 27
SP - 2383
EP - 2478
JO - Geometry and Topology
JF - Geometry and Topology
IS - 6
ER -