Shadows of mapping class groups: capturing convex cocompactness

2005/05/06 by Richard P. Kent, Richard P. Kent IV, Christopher J. Leininger +2 · 5 citations
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 #math.GR #math.GT #msc:20F65 #msc:30F60 #msc:57M07 #msc:57M50

paper · pdf · doi:10.48550/arxiv.math/0505114

v3. Final version accepted for publication. Minor revisions, updated references. v2. Theorems 3.9 and 3.10 strengthened, proof of Theorem 5.4 shortened, and questions in Section 8 modified. References to Brock--Farb, Duchin, and Hamenstadt added

openalex publication_date 2005/05/06 · arxiv created 2007/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We strengthen the analogy between convex co-compact Kleinian groups and convex co-compact subgroups of the mapping class group of a surface (in the sense of B. Farb and L. Mosher).

Citations

• Word hyperbolic extensions of surface groups
• Tameness of hyperbolic 3-manifolds
• The end of the curve complex

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• Subgroups of the mapping class group from the geometrical viewpoint
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• Undistorted purely pseudo-Anosov groups
• Some examples of separable convex-cocompact subgroups