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2019 On the nonrealizability of braid groups by homeomorphisms
Lei Chen
Geom. Topol. 23(7): 3735-3749 (2019). DOI: 10.2140/gt.2019.23.3735

Abstract

We show that the projection Homeo+(Dn2)Bn does not have a section for n6; ie the braid group Bn 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 g2.

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Lei Chen. "On the nonrealizability of braid groups by homeomorphisms." Geom. Topol. 23 (7) 3735 - 3749, 2019. https://doi.org/10.2140/gt.2019.23.3735

Information

Received: 26 August 2018; Revised: 2 April 2019; Accepted: 20 May 2019; Published: 2019
First available in Project Euclid: 7 January 2020

zbMATH: 07152168
MathSciNet: MR4047651
Digital Object Identifier: 10.2140/gt.2019.23.3735

Subjects:
Primary: 37E30, 57M60

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.23 • No. 7 • 2019
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