The hypoelliptic Laplacian on the cotangent bundle
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- by Jean-Michel Bismut;
- J. Amer. Math. Soc. 18 (2005), 379-476
- DOI: https://doi.org/10.1090/S0894-0347-05-00479-0
- Published electronically: February 28, 2005
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Abstract:
In this paper, we construct a new version of Hodge theory, where the corresponding Laplacian acts on the total space of the cotangent bundle. This Laplacian is a hypoelliptic operator, which is in general non-self-adjoint. When properly interpreted, it provides an interpolation between classical Hodge theory and the generator of the geodesic flow. The construction is also done in families in the superconnection formalism of Quillen and extends earlier work by Lott and the author.References
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Bibliographic Information
- Jean-Michel Bismut
- Affiliation: Département de Mathématique, Université Paris-Sud, Bâtiment 425, 91405 Orsay, France
- Email: Jean-Michel.Bismut@math.u-psud.fr
- Received by editor(s): February 9, 2004
- Published electronically: February 28, 2005
- Additional Notes: The author is indebted to Viviane Baladi, Sebastian Goette and Yves Le Jan for several discussions. Gilles Lebeau’s support and enthusiasm have been essential to the whole project. A referee has also provided much help by reading the manuscript very carefully.
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc. 18 (2005), 379-476
- MSC (2000): Primary 35H10, 58A14, 58J20
- DOI: https://doi.org/10.1090/S0894-0347-05-00479-0
- MathSciNet review: 2137981