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Teichmüller mapping class group of the universal hyperbolic solenoid

Marković, Vladimir and Šarić, Dragomir (2005) Teichmüller mapping class group of the universal hyperbolic solenoid. Transactions of the American Mathematical Society, 358 . pp. 2637-2650. ISSN 0002-9947. https://resolver.caltech.edu/CaltechAUTHORS:20170505-135946896

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Abstract

We show that the homotopy class of a quasiconformal self-map of the universal hyperbolic solenoid H_∞ is the same as its isotopy class and that the uniform convergence of quasiconformal self-maps of H_∞ to the identity forces them to be homotopic to conformal maps. We identify a dense subset of T(H_∞) such that the orbit under the base leaf preserving mapping class group MCG_(BLP)(H_∞) of any point in this subset has accumulation points in the Teichmüller space T(H_∞). Moreover, we show that finite subgroups of MCG_(BLP)(H_∞) are necessarily cyclic and that each point of T(H_∞) has an infinite isotropy subgroup in MCG_(BLP)(H_∞).


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1090/S0002-9947-05-03823-7DOIArticle
http://www.ams.org/journals/tran/2006-358-06/S0002-9947-05-03823-7/PublisherArticle
Additional Information:© 2005 American Mathematical Society. Received by the editors July 22, 2004. Article electronically published on October 31, 2005. We thank Francis Bonahon and Andy Miller for their useful comments.
Classification Code:2000 Mathematics Subject Classification. Primary 30F60; Secondary 32G05, 32G15, 37F30
Record Number:CaltechAUTHORS:20170505-135946896
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170505-135946896
Official Citation:Teichmüller mapping class group of the universal hyperbolic solenoid Vladimir Markovic and Dragomir Saric. Trans. Amer. Math. Soc. 358 (2006), 2637-2650
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77234
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:05 May 2017 22:08
Last Modified:03 Oct 2019 17:55

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