Ziggurats and rotation numbers
Danny Calegari Alden Walker
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.
keywords: 1-dimensional dynamics. rationality circle homeomorphism Arnol’d tongues rigidity ziggurat Rotation number
Geometry and topology of $\mathbb{R}$-covered foliations
Danny Calegari
keywords: Foliations laminations 3-manifolds group actions on R and S^1. geometrization product-covered R-covered

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