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arXiv · 2512.24136

Bicombing the mapping class group and Teichm\"uller space via stable cubical intervals

Matthew Gentry Durham
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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.

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Matthew Gentry Durham. 2025-12-30. Bicombing the mapping class group and Teichm\"uller space via stable cubical intervals. https://arxiv.org/abs/2512.24136

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