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Big mapping class groups and rigidity of the simple circle

Part of: Topological dynamics Low-dimensional dynamical systems Special aspects of infinite or finite groups Smooth dynamical systems: general theory

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

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, classification 37E10: Maps of the circle
Secondary: 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.) 37E45: Rotation numbers and vectors 20F05: Generators, relations, and presentations
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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