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Non-realizability of the Torelli group as area-preserving homeomorphisms

Chen, Lei and Markovic, Vladimir (2020) Non-realizability of the Torelli group as area-preserving homeomorphisms. Journal of the London Mathematical Society . ISSN 0024-6107. (In Press) https://resolver.caltech.edu/CaltechAUTHORS:20200717-084150079

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Abstract

Nielsen realization problem for the mapping class group Mod (S_g) asks whether the natural projection p_g: Homeo + (S_g) → Mod (S_g) has a section. While all the previous results use torsion elements in an essential way, in this paper, we focus on the much more difficult problem of realization of torsion‐free subgroups of Mod (S_g). The main result of this paper is that the Torelli group has no realization inside the area‐preserving homeomorphisms.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1112/jlms.12340DOIArticle
https://arxiv.org/abs/1904.09490arXivDiscussion Paper
ORCID:
AuthorORCID
Chen, Lei0000-0002-5941-7914
Additional Information:© 2020 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. Version of Record online: 28 June 2020; Manuscript revised: 31 March 2020; Manuscript received: 20 April 2019. V. Markovic was supported by the Simons Investigator Award 409745 from the Simons Foundation. We are in debt to the anonymous referee for many useful suggestions, extensive comments, in particular for schooling us about rotation numbers. We also thank Danny Calegari for useful discussions.
Funders:
Funding AgencyGrant Number
Simons Foundation409745
Classification Code:2010 Mathematics Subject Classification: 37E10, 37E30, 37E40 (primary)
Record Number:CaltechAUTHORS:20200717-084150079
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200717-084150079
Official Citation:Chen, L. and Markovic, V. (2020), Non‐realizability of the Torelli group as area‐preserving homeomorphisms. J. London Math. Soc.. doi:10.1112/jlms.12340
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104419
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:17 Jul 2020 16:01
Last Modified:17 Jul 2020 16:01

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