Geometry & Topology

On the nonrealizability of braid groups by homeomorphisms

Lei Chen

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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.

Article information

Source
Geom. Topol., Volume 23, Number 7 (2019), 3735-3749.

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1578366038

Digital Object Identifier
doi:10.2140/gt.2019.23.3735

Mathematical Reviews number (MathSciNet)
MR4047651

Zentralblatt MATH identifier
07152168

Subjects
Primary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces 57M60: Group actions in low dimensions

Keywords
dynamics of surfaces braid groups Nielsen realization

Citation

Chen, Lei. On the nonrealizability of braid groups by homeomorphisms. Geom. Topol. 23 (2019), no. 7, 3735--3749. doi:10.2140/gt.2019.23.3735. https://projecteuclid.org/euclid.gt/1578366038


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