An index theorem in differential K-theory

TL;DR

This paper establishes an index theorem in differential K-theory, showing that the analytic and topological indices of a differential K-theory class coincide for proper submersions with Riemannian structures.

Contribution

It introduces a new index theorem in differential K-theory, connecting analytic and topological indices in this refined cohomology theory.

Findings

Analytic and topological indices are equal in differential K-theory.

Defines indices for differential K-theory classes in the context of proper submersions.

Provides a rigorous proof of the index equality 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.