Flow Equivalence of Reducible Shifts of Finite Type

Using an invariant of Cuntz, we classify reducible shifts of nite type with two irre-ducible components up to ow equivalence. 0. Introduction Let A be an n n matrix over the non-negative integers Z +. Form a directed graph G A with n vertices and A(i; j) edges from vertex i to vertex j. Let E be the set of all edges of G A endowed with the discrete topology. Then the product space E Z is a compact zero-dimensional space. A shift of nite type (SFT) A : P A ! P A with adjacency matrix A is a homeomorphism A deened on the closed subset P A of E Z consisting of those innnite paths in G A : A matrix A over Z + is called irreducible if for each pair of (i; j), there is a k 2 N such that A k (i; j) > 0. It is called essentially irreducible if the maximum principal submatrix of A with no zero rows and columns is irreducible. Otherwise, it is called reducible. An irreducible matrix is called non-trivial, if it is not a cyclic permutation matrix. A reducible matrix is called indecomposable if every two irreducible components have a link in G A. A two-component SFT means a SFT whose adjacency matrix has exactly two irreducible components. Let h : X ! X be a homeomorphism on some topological space X. The standard suspension space of h is deened as the identiication space: