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- Title
Eta invariants and the hypoelliptic Laplacian.
- Authors
Bismut, Jean-Michel
- Abstract
The purpose of this paper is to give a new proof of the results of Moscovici and Stanton on orbital integrals associated with eta invariants on compact locally symmetric spaces. Moscovici and Stanton used methods of harmonic analysis on reductive groups. Here, we combine our approach to orbital integrals that uses the hypoelliptic Laplacian with the introduction of a rotation on certain Clifford algebras. Probabilistic methods play an important role in establishing key estimates. In particular, we construct a suitable Ito calculus associated with certain hypoelliptic diffusions.
- Subjects
ORBITAL interaction; HYPOELLIPTIC operators; GRAPHIC methods; TOPOLOGICAL algebras; INVARIANTS (Mathematics)
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2019, Vol 21, Issue 8, p2355
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/887