Volume 23, issue 7 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 7, 3233–3749
Issue 6, 2701–3231
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
On the nonrealizability of braid groups by homeomorphisms

Lei Chen

Geometry & Topology 23 (2019) 3735–3749
Abstract

We show that the projection Homeo+(Dn2) Bn does not have a section for n 6; 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 g 2.

Keywords
dynamics of surfaces, braid groups, Nielsen realization
Mathematical Subject Classification 2010
Primary: 37E30, 57M60
References
Publication
Received: 26 August 2018
Revised: 2 April 2019
Accepted: 20 May 2019
Published: 30 December 2019
Proposed: Ian Agol
Seconded: Anna Wienhard, John Lott
Authors
Lei Chen
Department of Mathematics
California Institute of Technology
Pasadena, CA
United States