On Embedding of the Bratteli Diagram into a Surface.

We study C*-algebras Oλ 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. [ABSTRACT FROM AUTHOR]