Subgroups of the mapping class group from the geometrical viewpoint

2007/02/01 by Richard P. Kent, Christopher J. Leininger, Kent, Richard P. +1
Mathematics · #20F65 (Primary) #30F60 #57M07 #57M50 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/0702034

openalex publication_date 2007/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We survey the analogy between Kleinian groups and subgroups of the mapping class group of a surface.

Citations

• Thin triangles and a multiplicative ergodic theorem for Teichmüller geometry
• A simple criterion for non-relative hyperbolicity and one-endedness of groups
• Tameness of hyperbolic 3-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

Related

• Geometric survey of subgroups of mapping class groups
• Geometric subgroups of mapping class groups
• Problems, Questions, and Conjectures about Mapping Class Groups
• Shadows of mapping class groups: capturing convex cocompactness
• Different versions of mapping class groups of surfaces