An interesting example for spectral invariants
Résumé
In "Illinois J. of Math. {\bf 38} (1994) 653--678", 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 showed that the associated heat operator converges to the Chern character of the index bundle of the operator. In "J. K-Theory {\bf 1} (2008) 305--356", we improved this result 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.
Domaines
Topologie géométrique [math.GT]Format du dépôt | Notice |
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Type de dépôt | Article dans une revue |
Titre |
en
An interesting example for spectral invariants
|
Résumé |
en
In "Illinois J. of Math. {\bf 38} (1994) 653--678", 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 showed that the associated heat operator converges to the Chern character of the index bundle of the operator. In "J. K-Theory {\bf 1} (2008) 305--356", we improved this result 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.
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Auteur(s) |
Moulay Tahar Benameur
1
, J. L. Heitsch
2
, Charlotte Wahl
3
1
I3M -
Institut de Mathématiques et de Modélisation de Montpellier
( 631 )
- Case Courrier 051 Place Eugène Bataillon 34095 MONTPELLIER CEDEX 5
- France
2
UIC -
University of Illinois [Chicago]
( 367491 )
- 1200 West Harrison St.,
Chicago, Illinois 60607
- États-Unis
3
Leibniz Universität Hannover=Leibniz University Hannover
( 326198 )
- Gottfried Wilhelm Leibniz Universität Hannover
Postfach 6009
30060 Hannover
- Allemagne
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Comité de lecture |
Oui
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Vulgarisation |
Non
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Nom de la revue |
|
Volume |
13
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Audience |
Internationale
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Date de publication |
2014-04-01
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Page/Identifiant |
305-311
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Numéro |
2
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Langue du document |
Anglais
|
Commentaire |
Third author added. Some typos corrected and some material added
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Domaine(s) |
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arXiv Id | 1304.7086 |
DOI | 10.1017/is014002020jkt255 |
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