Trees and mapping class groups

Richard P. Kent, Christopher J. Leininger, Saul Schleimer

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1-21
Number of pages21
JournalJournal fur die Reine und Angewandte Mathematik
Issue number637
DOIs
StatePublished - Dec 2009

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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