#### Volume 14, issue 2 (2010)

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An index theorem in differential $K$–theory

### Daniel S Freed and John Lott

Geometry & Topology 14 (2010) 903–966
##### Abstract

Let $\pi :X\to B$ 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.

 To our teacher Isadore Singer on the occasion of his 85th birthday
##### Keywords
index theory, Dirac operator, differential $K$–theory
##### Mathematical Subject Classification 2000
Primary: 58J22
Secondary: 19K56, 19L99