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index bundle

Journal of K-Theory (1)

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Index Theory and Non-Commutative Geometry II. Dirac Operators and Index Bundles
Moulay-Tahar Benameur, James L. Heitsch
Journal:

Journal of K-Theory / Volume 1 / Issue 2 / April 2008

Published online by Cambridge University Press:

30 November 2007, pp. 305-356

Print publication:

April 2008
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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.