## Geometry & Topology

### An index theorem in differential $K$–theory

#### Abstract

Let $π:X→B$ 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.

#### Article information

Source
Geom. Topol., Volume 14, Number 2 (2010), 903-966.

Dates
Revised: 7 January 2010
Accepted: 24 December 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732209

Digital Object Identifier
doi:10.2140/gt.2010.14.903

Mathematical Reviews number (MathSciNet)
MR2602854

Zentralblatt MATH identifier
1197.58007

#### Citation

Freed, Daniel S; Lott, John. An index theorem in differential $K$–theory. Geom. Topol. 14 (2010), no. 2, 903--966. doi:10.2140/gt.2010.14.903. https://projecteuclid.org/euclid.gt/1513732209

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