%0 Journal Article
%T On embedding of the Bratteli diagram into a surface
%A Igor Nikolaev
%J Mathematics
%D 2001
%I arXiv
%R 10.1007/978-3-7643-8539-2_13
%X 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.
%U http://arxiv.org/abs/math/0104082v3