Volume 14, issue 2 (2010)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
An index theorem in differential $K$–theory

Daniel S Freed and John Lott

Geometry & Topology 14 (2010) 903–966
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.

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
References
Publication
Received: 25 July 2009
Revised: 7 January 2010
Accepted: 24 December 2009
Published: 5 March 2010
Proposed: Peter Teichner
Seconded: Ralph Cohen, Simon Donaldson
Authors
Daniel S Freed
Department of Mathematics
University of Texas
1 University Station C1200
Austin, TX 78712-0257
USA
John Lott
Department of Mathematics
University of California, Berkeley
970 Evans Hall #3840
Berkeley, CA 94720-3840
USA