On embedding of the Bratteli diagram into a surface

Details On embedding of the Bratteli diagram into a surface On embedding of the Bratteli diagram into a surface

2001-04-06

arxiv.org/abs/math/0104082v3

Recent Advances in Matrix and Operator Theory 179 (2008), pp 211-227; Birkhauser

Mathematics

K-Theory and Homology

final version

Scientific paper

10.1007/978-3-7643-8539-2_13

We study C*-algebras O_{\lambda} 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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