Trees and mapping class groups

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

Trees and mapping class groups

Authors

Kent IV, Richard P.

Leininger, Christopher J.

Schleimer, Saul

Description

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.
v2. Completely reorganized and rewritten; 22 pages. Revision includes new proofs of theorems of Kra an Harer. v1. 18 pages