Geometry & Topology

On the nonrealizability of braid groups by homeomorphisms

Lei Chen

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

dynamics of surfaces braid groups Nielsen realization


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.

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