Superconnections and index theory

We investigate index theory in the context of Dirac operators coupled to superconnections. In particular, we prove a local index theorem for such operators, and for families of such operators. We investigate eta-invariants and prove an APS theorem, and construct a geometric determinant line bundle for families of such operators, computing its curvature and holonomy in terms of familiar index theoretic quantities. (C) 2011 Elsevier B.V. All rights reserved.