Ziggurats and rotation numbers

Danny Calegari; Alden Walker

doi:10.3934/jmd.2011.5.711

Article Contents

2011, Volume 5, Issue 4: 711-746. Doi: 10.3934/jmd.2011.5.711

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Ziggurats and rotation numbers

Danny Calegari^1, and
Alden Walker^2,

1.
DPMMS, University of Cambridge, Cambridge CB3 0WA
2.
Department of Mathematics, California Institute of Technology, Pasadena, CA 91125

Received: October 2011

Revised: November 2011

Published: February 2012

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Abstract

We establish the existence of new rigidity and rationality phenomena in the theory of nonabelian group actions on the circle and introduce tools to translate questions about the existence of actions with prescribed dynamics into finite combinatorics. A special case of our theory gives a very short new proof of Naimi's theorem (i.e., the conjecture of Jankins-Neumann) which was the last step in the classification of taut foliations of Seifert fibered spaces.

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Mathematics Subject Classification: Primary: 37E45, 58D05; Secondary: 58F10.

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