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On embedding of the Bratteli diagram into a surface

Igor Nikolaev
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Abstract

We study C*-algebras O_λ which arise in dynamics of the interval exchange transformations and measured foliations on compact surfaces. Using Koebe-Morse coding of geodesic lines, we establish a bijection between Bratteli diagrams of such algebras and measured foliations. This approach allows us to apply K-theory of operator algebras to prove strict ergodicity criterion and Keane's conjecture for the interval exchange transformations.

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Igor Nikolaev. 2009-01-19. On embedding of the Bratteli diagram into a surface. https://doi.org/10.1007/978-3-7643-8539-2_13

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