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An interesting example for spectral invariants

Published online by Cambridge University Press:  03 April 2014

Moulay-Tahar Benameur ,
James L. Heitsch  and
Charlotte Wahl
Moulay-Tahar Benameur
Affiliation:
I3M UMR 5149 du CNRS, Université de Montpellier 2, 34095 Montpellier, France, moulay.benameur@univ–montp2.fr
James L. Heitsch
Affiliation:
Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Mathematics, Northwestern University, USA, heitsch@math.uic.edu
Charlotte Wahl
Affiliation:
Leibniz-Archiv, Waterloostr. 8, 30169 Hannover, Germany, wahlcharlotte@gmail.com
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Abstract

In [HL99], the heat operator of a Bismut superconnection for a family of generalized Dirac operators is defined along the leaves of a foliation with Hausdorff groupoid. The Novikov-Shubin invariants of the Dirac operators were assumed greater than three times the codimension of the foliation. It was then shown that the associated heat operator converges to the Chern character of the index bundle of the operator. In [BH08], this result was improved by reducing the requirement on the Novikov-Shubin invariants to one half of the codimension. In this paper, we construct examples which show that this is the best possible result.

Keywords

spectral invariantsfoliationsDirac operatorsindex theory58J2219K5646L8058J42

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Type
Research Article
Information
Journal of K-Theory , Volume 13 , Issue 2 , April 2014 , pp. 305 - 311
Copyright
Copyright © ISOPP 2014 

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References

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