Bicombing Mapping Class Groups and Teichmüller Space
Published:Dec 30, 2025 10:45
•1 min read
•ArXiv
Analysis
This paper provides a new and simplified approach to proving that mapping class groups and Teichmüller spaces admit bicombings. The result is significant because bicombings are a useful tool for studying the geometry of these spaces. The paper also generalizes the result to a broader class of spaces called colorable hierarchically hyperbolic spaces, offering a quasi-isometric relationship to CAT(0) cube complexes. The focus on simplification and new aspects suggests an effort to make the proof more accessible and potentially improve existing understanding.
Key Takeaways
- •Provides a new proof of bicombings for mapping class groups and Teichmüller spaces.
- •Offers a simplified and novel approach to the proof.
- •Generalizes the result to colorable hierarchically hyperbolic spaces.
- •Establishes a quasi-isometric relationship to CAT(0) cube complexes.
Reference
“The paper explains 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.”