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Realization of the mapping class group by homeomorphisms

Markovic, Vladimir (2007) Realization of the mapping class group by homeomorphisms. Inventiones Mathematicae, 168 (3). pp. 523-566. ISSN 0020-9910.

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In this paper, we show that the mapping class group of a closed surface can not be geometrically realized as a group of homeomorphisms of that surface. More precisely, let Pr:Homeo(M)→MC(M) denote the standard projection of the group of homeomorphisms to the mapping class group of a closed surface M of genus g>5. We show that there is no homomorphism E:MC(M)→Homeo(M), such that Pr∘E is the identity. This answers a question by Thurston (see [11]).

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Additional Information:© 2007 Springer-Verlag. Received: 01 July 2006; Accepted: 18 January 2007; First Online: 07 March 2007.
Issue or Number:3
Classification Code:Mathematics Subject Classification (2000): Primary 20H10, 37F30
Record Number:CaltechAUTHORS:20170508-092249054
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Official Citation:Markovic, V. Invent. math. (2007) 168: 523. doi:10.1007/s00222-007-0039-0
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77251
Deposited By: Tony Diaz
Deposited On:09 May 2017 21:55
Last Modified:03 Oct 2019 17:55

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