An index theorem in differential K–theory

Freed, Daniel S; Lott, John

doi:10.2140/gt.2010.14.903

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An index theorem in differential $K$–theory

Daniel S Freed and John Lott

Geometry & Topology 14 (2010) 903–966

DOI: 10.2140/gt.2010.14.903

Abstract

Let $π : X \to B$ 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

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

Volume 14, issue 2 (2010)