Product formula for Atiyah-Patodi-Singer index classes and higher signatures

Abstract

Abstract We define generalized Atiyah-Patodi-Singer boundary conditions of product type for Dirac operators associated to C *-vector bundles on the product of a compact manifold with boundary and a closed manifold. We prove a product formula for the K -theoretic index classes, which we use to generalize the product formula for the topological signature to higher signatures.