Published December 30, 2019
| Version Submitted + Published
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On the nonrealizability of braid groups by homeomorphisms
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Abstract
We show that the projection Homeo_+(D²_n)→B_n does not have a section for n ≥ 6; ie the braid group B_n cannot be geometrically realized as a group of homeomorphisms of a disk fixing the boundary pointwise and n marked points in the interior as a set. We also give a new proof of a result of Markovic (2007) that the mapping class group of a surface of genus g cannot be geometrically realized as a group of homeomorphisms when g ≥ 2.
Additional Information
© 2019 Mathematical Sciences Publishers. Received: 26 August 2018; Revised: 2 April 2019; Accepted: 20 May 2019; Published: 30 December 2019. Proposed: Ian Agol; Seconded: Anna Wienhard, John Lott. This project obtained ideas from a previous paper with Nick Salter [4] about torsion elements of spherical braid group. The author thanks Benson Farb, Nick Salter and Bena Tshishiku for asking the question about the lifting braid group in the Oberwolfach 2016 conference on surface bundles; she thanks Benson Farb, Dan Margalit and Nick Salter for discussions and comments on the paper. She would also like to thank Vlad Markovic for very useful discussions and the anonymous referee for suggestions on the paper.Attached Files
Published - gt-v23-n7-p11-p.pdf
Submitted - 1808.08248v2.pdf
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1808.08248v2.pdf
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Additional titles
- Alternative title
- On the non-realizability of braid groups by homeomorphisms
Identifiers
- Eprint ID
- 100883
- Resolver ID
- CaltechAUTHORS:20200124-081733746
Related works
- Describes
- https://arxiv.org/abs/1808.08248 (URL)
Dates
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2020-01-24Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field