Classification of Cuntz Krieger algebras by orbit equivalence of topological Markov shifts
Let A,B be square irreducible matrices with entries in {0, 1} Assume that the determinants of 1 A and 1 B have the same sign. We will show that the Cuntz Krieger algebras OA and OB are isomorphic if and only if the right one sided topological Markov shifts (XA, sA) and (XB sB) are continuously orbit equivalent.