Ziggurats and rotation numbers | Zendy

Danny Calegari | Zendy; Alden Walker | Zendy

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Ziggurats and rotation numbers

Author(s) -

Danny Calegari,

Alden Walker

Publication year - 2011

Publication title -

journal of modern dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.668

H-Index - 25

eISSN - 1930-532X

pISSN - 1930-5311

DOI - 10.3934/jmd.2011.5.711

Subject(s) - mathematics , rigidity (electromagnetism) , fibered knot , von neumann architecture , rationality , pure mathematics , group action , group (periodic table) , algebra over a field , chemistry , structural engineering , organic chemistry , political science , law , engineering

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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