E-theory for C[0, 1]-algebras with finitely many singular points

Abstract

Abstract. We study the E-theory group E [0,1] (A(x), B(y)) = 0 for all x, y ∈ [0, 1]. This result applies whenever the fibers satisfy the UCT, their K0-groups are free of finite rank and their K1-groups are zero. In that case we show that E [0,1] (A, B) is isomorphic to Hom(K0(A), K0(B)), the group of morphisms of the K-theory sheaves of A and B. As an application, we give a streamlined partially new proof of a classification result due to the first author and Elliott.