## Abstract

Let X and Y be two closed connected Riemannian manifolds of the same dimension and ϕ : S*X → S*Y a contact diffeomorphism. We show that the index of an elliptic Fourier operator Φ associated with ϕ is given by ∫_{B*(X)} e^{θ0} Â(T*X) − ∫_{B*(Y)} e^{θ0} Â(T*Y) where θ_{0} is a certain characteristic class depending on the principal symbol of Φ and, B*(X) and B*(Y) are the unit ball bundles of the manifolds X and Y . The proof uses the algebraic index theorem of Nest-Tsygan for symplectic Lie Algebroids and an idea of Paul Bressler to express the index of Φ as a trace of 1 in an appropriate deformed algebra. In the special case when X = Y we obtain a different proof of a theorem of Epstein-Melrose conjectured by Atiyah and Weinstein.

Original language | English (US) |
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Pages (from-to) | 269-300 |

Number of pages | 32 |

Journal | Journal of Differential Geometry |

Volume | 59 |

Issue number | 2 |

DOIs | |

State | Published - 2001 |

## ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory
- Geometry and Topology