2006/11/08 by Richard P. Kent, Richard P. Kent IV, Kent, Richard P. +4 · 1 citation
Computer Science · Mathematics · #20F65 (Primary) #20F67 #57M07 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR #math.GT #msc:20F65 #msc:20F67 #msc:57M07 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0611241
v2. Completely reorganized and rewritten; 22 pages. Revision includes new proofs of theorems of Kra an Harer. v1. 18 pages
openalex publication_date 2006/11/08 · arxiv created 2007/09/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There is a forgetful map from the mapping class group of a punctured surface to that of the surface with one fewer puncture. We prove that finitely generated purely pseudo-Anosov subgroups of the kernel of this map are convex cocompact in the sense of B. Farb and L. Mosher. In particular, we obtain an affirmative answer to their question of local convex cocompactness of K. Whittlesey's group. In the course of the proof, we obtain a new proof of a theorem of I. Kra. We also relate the action of this kernel on the curve complex to a family of actions on trees. This quickly yields a new proof of a theorem of J. Harer.