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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Discontinuity-growth of interval-exchange maps
TL;DR: In this article, it was shown that the group of interval exchange maps does not contain distortion elements, giving examples of groups that do not act faithfully via interval exchange map and a classification of centralizers.
Posted Content
Non-ergodic Z-periodic billiards and infinite translation surfaces
TL;DR: In this article, the authors give a criterion which allows to prove non-ergodicity for certain infinite periodic billiards and directional flows on Z-periodic translation surfaces.
Journal ArticleDOI
Injections of mapping class groups
TL;DR: In this paper, the authors construct monomorphisms between mapping class groups of surfaces, which injects the mapping class group of a closed surface into that of a different closed surface, and have quite curious behaviour.
Book
Hyperbolic Manifolds: An Introduction in 2 and 3 Dimensions
TL;DR: In this article, the authors introduce and explain hyperbolic geometry and 3-manifolds in the first two chapters and then go on to develop the subject in the last two.
References
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Gauss measures for transformations on the space of interval exchange maps
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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.