An index theorem in differential K-theory

Abstract

Let X --> B be a proper submersion with a Riemannian structure. Given a differential K-theory class on X, we define its analytic and topological indices as differential K-theory classes on B. We prove that the two indices are the same.

65 pages; version 2 has small changes for publication

Cited by in corpus (14)

• Reflection positivity and invertible topological phases
• Spectral sequences in smooth generalized cohomology
• Regulators and cycle maps in higher-dimensional differential algebraic K-theory
• A Geometric Model for Odd Differential K-theory
• Geometric models of twisted differential K-theory I
• The differential analytic index in Simons-Sullivan differential K-theory
• Geometric Aspects of D-branes and T-duality
• The Caloron Correspondence and Odd Differential K-theory
• Noncommutative Differential K-theory
• Flat pairing and generalized Cheeger-Simons characters
• The flat Grothendieck-Riemann-Roch theorem without adiabatic techniques
• Twisted differential K-characters and D-branes
• Induced $C^{\ast }$-complexes in metaplectic geometry
• Characters for Complex Bundles and their Connections