Geometry & Topology
- Geom. Topol.
- Volume 23, Number 7 (2019), 3735-3749.
On the nonrealizability of braid groups by homeomorphisms
We show that the projection does not have a section for ; ie the braid group cannot be geometrically realized as a group of homeomorphisms of a disk fixing the boundary pointwise and 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 cannot be geometrically realized as a group of homeomorphisms when .
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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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