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The Birman exact sequence does not virtually split

Chen, Lei and Salter, Nick (2021) The Birman exact sequence does not virtually split. Mathematical Research Letters, 28 (2). pp. 383-413. ISSN 1073-2780. doi:10.4310/mrl.2021.v28.n2.a3.

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This paper answers a basic question about the Birman exact sequence in the theory of mapping class groups. We prove that the Birman exact sequence does not admit a section over any subgroup Γ contained in the Torelli group with finite index. A fortiori this implies that there is no multi-section for the universal surface bundle with Torelli monodromy. This theorem was announced in a 1990 preprint of G. Mess, but an error was uncovered and described in a recent paper of the first author.

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Chen, Lei0000-0002-5941-7914
Additional Information:© 2021 International Press. Received 8 January 2019; Accepted 24 February 2020; Published 13 May 2021. NS is supported by the National Science Foundation under Award No. DMS-1703181. The first author would like to thank Jonathan Bowden for discussing the content of the paper of Mess and possible fixes during the Oberwolfach meeting on surface bundles in 2016 and afterwards. Both authors would like to thank an anonymous referee for comments that greatly improved the paper.
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Issue or Number:2
Record Number:CaltechAUTHORS:20210610-131429400
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109469
Deposited By: Tony Diaz
Deposited On:10 Jun 2021 20:36
Last Modified:10 Jun 2021 20:36

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