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Trees and mapping class groups

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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. ISSN 0075-4102

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Official URL: http://dx.doi.org/10.1515/CRELLE.2009.087

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:

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)

References:

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