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Rigidity of mapping class
group actions on $S^1$
Kathryn Mann and Maxime Wolff |
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Geometry & Topology 24 (2020) 1211–1223
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Abstract |
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The mapping class group of a surface with one marked point can be identified with an index two subgroup of . For a surface of genus , we show that any action of on the circle is either semiconjugate to its natural faithful action on the Gromov boundary of , or factors through a finite cyclic group. For , 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
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Mathematical Subject Classification 2010
Primary: 57M60
Secondary: 20F34, 57M07
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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
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Authors |
| Kathryn Mann | |
| Department of Mathematics Cornell University Ithaca, NY United States |
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| Maxime Wolff | |
| Sorbonne Universités UPMC Univ. Paris 06 Institut de Mathématiques de Jussieu-Paris Rive Gauche UMR 7586 CNRS Univ. Paris Diderot Paris France |
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