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Big mapping class groups and rigidity of the simple circle

Part of:Smooth dynamical systems: general theoryLow-dimensional dynamical systemsTopological dynamicsSpecial aspects of infinite or finite groups

Published online by Cambridge University Press:  03 June 2020

DANNY CALEGARI and
LVZHOU CHEN
DANNY CALEGARI
Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois, USA email dannyc@math.uchicago.edu, lzchen@math.uchicago.edu
LVZHOU CHEN
Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois, USA email dannyc@math.uchicago.edu, lzchen@math.uchicago.edu
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Abstract

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Let $\unicode[STIX]{x1D6E4}$ denote the mapping class group of the plane minus a Cantor set. We show that every action of $\unicode[STIX]{x1D6E4}$ on the circle is either trivial or semiconjugate to a unique minimal action on the so-called simple circle.

Keywords

group actionslow-dimensional dynamicsbig mapping class groupsrigidity

MSC classification

Primary:37C15: Topological and differentiable equivalence, conjugacy, invariants, moduli, classification37E10: Maps of the circle
Secondary:37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)37E45: Rotation numbers and vectors20F05: Generators, relations, and presentations

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 7 , July 2021, pp. 1961 - 1987
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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