Curve complex as a coset intersection complex

2025/10/28 by He, Haoyang, Martínez-Pedroza, Eduardo
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2510.23955

Abstract

We show that, for every finitely generated group quasi-isometric to the mapping class group of a surface, there is a collection of subgroups such that their coset intersection complex is combinatorially equivalent to the curve complex, in the sense that one can be obtained from the other via taking a nerve. We also prove that the automorphism group of this coset intersection complex is the extended mapping class group, providing new evidence for Ivanov's metaconjecture.

Citations

• Homotopy types of complexes of hyperplanes in quasi-median graphs and applications to right-angled Artin groups
• The quasi-isometry invariance of the Coset Intersection Complex
• The model theory of the curve graph
• Cubical-like geometry of quasi-median graphs and applications to geometric group theory
• Normal subgroups of mapping class groups and the metaconjecture of Ivanov
• On the ideal triangulation graph of a punctured surface
• Geometry and rigidity of mapping class groups
• Fifteen problems about the mapping class groups
• Injective Simplicial Maps of the Arc Complex
• Geometry of the mapping class groups III: Quasi-isometric rigidity
• The classification of Kleinian surface groups, II: The Ending Lamination Conjecture
• Automorphisms of the Hatcher-Thurston complex
• Complexes of Nonseparating Curves and Mapping Class Groups
• The classification of Kleinian surface groups, I: Models and bounds
• Curvature and rank of Teichmüller space
• Automorphisms of the Complex of Curves

Related

• The quasi-isometry invariance of the Coset Intersection Complex
• Geometry and rigidity of mapping class groups
• Automorphisms of the fine curve graph
• Automorphisms of the fine curve graph
• Combinatorial rigidity in curve complexes and mapping class groups