2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216404We 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.final versionK-Theory and HomologyOperator Algebras19K14; 46L40; 57R30text