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Index Theory and Non-Commutative Geometry II. Dirac Operators and Index Bundles

Published online by Cambridge University Press:  30 November 2007

Moulay-Tahar Benameur  and
James L. Heitsch
Moulay-Tahar Benameur
Affiliation:
benameur@math.univ-metz.fr UMR 7122 du CNRS, Université de Metz, Ile du Saulcy, Metz, France
James L. Heitsch
Affiliation:
heitsch@math.uic.edu, j-heitsch@northwestern.edu Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Mathematics Northwestern University
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Abstract

When the index bundle of a longitudinal Dirac type operator is transversely smooth, we define its Chern character in Haefliger cohomology and relate it to the Chern character of the K—theory index. This result gives a concrete connection between the topology of the foliation and the longitudinal index formula. Moreover, the usual spectral assumption on the Novikov-Shubin invariants of the operator is improved.

Keywords

Non-commutative geometryfoliationindex theoryDirac operatorindex bundle

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Type
Research Article
Information
Journal of K-Theory , Volume 1 , Issue 2 , April 2008 , pp. 305 - 356
Copyright
Copyright © ISOPP 2008

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