Kent, Richard P., Leininger, Christopher J. and Schleimer, Saul (2009) Trees and mapping class groups. Journal fur die reine und angewandte Mathematik, Vol.2009 (No.637). pp. 1-21. doi:10.1515/CRELLE.2009.087

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Mappings (Mathematics), Surfaces, Kernel functions
Journal or Publication Title:	Journal fur die reine und angewandte Mathematik
Publisher:	Walter de Gruyter & Co
ISSN:	0075-4102
Official Date:	December 2009
Dates:	Date Event December 2009 Published
Volume:	Vol.2009
Number:	No.637
Number of Pages:	21
Page Range:	pp. 1-21
DOI:	10.1515/CRELLE.2009.087
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	National Science Foundation (U.S.) (NSF)
Grant number:	DMS-0603881 (NSF), DMS-0508971 (NSF)

Data sourced from Thomson Reuters' Web of Knowledge

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