Journal ArticleDOI
Interval Exchange Transformations and Measured Foliations
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This article is published in Annals of Mathematics.The article was published on 1982-01-01. It has received 851 citations till now. The article focuses on the topics: Interval exchange transformation & Interval (graph theory).read more
Citations
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Coding Teichmüller flow using veering triangulations
TL;DR: In this article, the theory of veering triangulations on oriented surfaces adapted to half-translation surfaces was developed and used to give a coding of the Teichmuller flow on connected components of strata of quadratic differentials.
Book ChapterDOI
Stabilizer and Maximality
TL;DR: In this article, the relation between the stabilizer of the graph of the Teichmuller curve and the commensurator of the Veech group is described.
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Single-cylinder square-tiled surfaces and the ubiquity of ratio-optimising pseudo-Anosovs
TL;DR: In this article, it was shown that pseudo-Anosov homeomorphisms optimising the ratio of Teichmueller to curve graph translation length are ubiquitous in the connected components of strata of Abelian differentials.
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Exactness of the Euclidean algorithm and of the Rauzy induction on the space of interval exchange transfomations
TL;DR: The Rauzy induction, a generalization of the Euclidean algorithm, is a key tool in the study of interval exchange transformations as mentioned in this paper, and it is known that both maps are exact.
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Riemann surfaces: noncommutative story
TL;DR: For an open and dense subset in the Teichmüller space, the authors introduced a coordinate system which is well-behaved under the action of the mapping class group.
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Journal ArticleDOI
Gauss measures for transformations on the space of interval exchange maps
Journal ArticleDOI
Quadratic differentials and foliations
John H. Hubbard,Howard Masur +1 more
TL;DR: In this paper, it was shown that the space of measured foliations with the quadratic forms on a fixed Riemann surface is homeomorphic to a sphere, and that the existence of projective classes of foliations is also homeomorphic.