Volume 24, issue 3 (2020)

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

Volume 25
Issue 5, 2167–2711
Issue 4, 1631–2166
Issue 3, 1087–1630
Issue 2, 547–1085
Issue 1, 1–546

Volume 24, 7 issues

Volume 23, 7 issues

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
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Rigidity of mapping class group actions on $S^1$

Kathryn Mann and Maxime Wolff

Geometry & Topology 24 (2020) 1211–1223
Abstract

The mapping class group Modg,1 of a surface with one marked point can be identified with an index two subgroup of Aut(π1Σg). For a surface of genus g 2, we show that any action of Modg,1 on the circle is either semiconjugate to its natural faithful action on the Gromov boundary of π1Σg, or factors through a finite cyclic group. For g 3, all finite actions are trivial. This answers a question of Farb.

Keywords
mapping class group, Gromov boundary, surface group, rigidity, homeomorphisms of the circle, Euler class
Mathematical Subject Classification 2010
Primary: 57M60
Secondary: 20F34, 57M07
References
Publication
Received: 15 September 2018
Revised: 28 May 2019
Accepted: 11 October 2019
Published: 30 September 2020
Proposed: Jean-Pierre Otal
Seconded: John Lott, Ulrike Tillmann
Authors
Kathryn Mann
Department of Mathematics
Cornell University
Ithaca, NY
United States
Maxime Wolff
Sorbonne Universités
UPMC Univ. Paris 06
Institut de Mathématiques de Jussieu-Paris Rive Gauche
UMR 7586
CNRS
Univ. Paris Diderot
Paris
France