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Rigidity and geometricity
for surface group actions on the circle
Kathryn Mann and Maxime Wolff |
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Geometry & Topology 28 (2024) 2345–2398
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Abstract |
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We prove that (topologically) rigid actions of surface groups on the circle by homeomorphisms are necessarily geometric, namely, they are semiconjugate to an embedding as a cocompact lattice in a Lie group acting transitively on . This gives the converse to a theorem of the first author; thus characterizing geometric actions as the unique isolated points in the “character space” of surface group actions on . |
Keywords
surface group, circle homeomorphism, Euler class, rigidity,
representation space
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Mathematical Subject Classification
Primary: 20H10, 37E10, 37E45, 57S25, 58D29
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References |
Publication
Received: 20 September 2022
Revised: 28 November 2022
Accepted: 28 December 2022
Published: 24 August 2024
Proposed: David Fisher
Seconded: Leonid Polterovich, Dan Abramovich
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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 Sorbonne Paris Cité Paris France |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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