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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. doi:10.1515/CRELLE.2009.087 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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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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 (Creative Commons) | ||||
Date of first compliant deposit: | 8 December 2015 | ||||
Date of first compliant Open Access: | 8 December 2015 | ||||
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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