2001/04/30 by Igor Nikolaev
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Artificial intelligence #Bijection #Combinatorics #Computer science #Conjecture #Discrete mathematics #Embedding #Geodesic #Interval (graph theory) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Operator (biology) #Pure mathematics #math.KT #math.OA #msc:19K14 #msc:46L40 #msc:57R30
paper · pdf · doi:10.1007/978-3-7643-8539-2_13
published as Recent Advances in Matrix and Operator Theory 179 (2008), pp 211-227; Birkhauser · final version
openalex publication_date 2007/12/21 · arxiv created 2009/01/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.