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Realization of the mapping class group by homeomorphisms
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Markovic, Vladimir (2007) Realization of the mapping class group by homeomorphisms. Inventiones Mathematicae, Vol.168 (No.3). pp. 523-566. doi:10.1007/s00222-007-0039-0 ISSN 0020-9910.
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Official URL: http://dx.doi.org/10.1007/s00222-007-0039-0
Abstract
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 epsilon : MC(M) -> Homeo(M), such that Pr circle epsilon is the identity. This answers a question by Thurston (see [11]).
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Inventiones Mathematicae | ||||
| Publisher: | Springer | ||||
| ISSN: | 0020-9910 | ||||
| Official Date: | June 2007 | ||||
| Dates: |
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| Volume: | Vol.168 | ||||
| Number: | No.3 | ||||
| Number of Pages: | 44 | ||||
| Page Range: | pp. 523-566 | ||||
| DOI: | 10.1007/s00222-007-0039-0 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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