Geometry & Topology

An index theorem in differential $K$–theory

Daniel S Freed and John Lott

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Abstract

Let π:XB 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
Received: 25 July 2009
Revised: 7 January 2010
Accepted: 24 December 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
Primary: 58J22: Exotic index theories [See also 19K56, 46L05, 46L10, 46L80, 46M20]
Secondary: 19K56: Index theory [See also 58J20, 58J22] 19L99: None of the above, but in this section

Keywords
index theory Dirac operator differential $K$–theory

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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