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 a strict ergodicity criterion and Keane’s conjecture for the interval exchange transformations.
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© 2007 Birkhäuser Verlag Basel/Switzerland
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Nikolaev, I.V. (2007). On Embedding of the Bratteli Diagram into a Surface. In: Ball, J.A., Eidelman, Y., Helton, J.W., Olshevsky, V., Rovnyak, J. (eds) Recent Advances in Matrix and Operator Theory. Operator Theory: Advances and Applications, vol 179. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8539-2_13
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DOI: https://doi.org/10.1007/978-3-7643-8539-2_13
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