Superconnections and Index Theory

Abstract

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.

29 pages, 1 figure; minor updates and corrections; final version

References in corpus (3)

• Setting the quantum integrand of M-theory
• Superconnections and Index Theory
• Flux corrections to anomaly cancellation in M-theory on a manifold with boundary

Cited by in corpus (6)

• Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
• Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
• Higher Berry Phase of Fermions and Index Theorem
• Superconnections and Index Theory
• Coupling of gravity to matter, spectral action and cosmic topology
• Anomaly and Superconnection