Local formula for the index of a Fourier Integral Operator

Details Local formula for the index of a Fourier Integral Operator Local formula for the index of a Fourier Integral Operator

2000-04-05

arxiv.org/abs/math/0004022v1

Mathematics

Differential Geometry

25 pages, preprint

Scientific paper

We show that the index of an elliptic Fourier integral operator associated to a contact diffeomorphism $\phi$ of cosphere bundles of two Riemannian manifolds X and Y is given by $\int_{B^*X}\hat{A}(T^*X)\exp{\theta} - \int_{B^*Y}\hat{A}(T^*Y)\exp{\theta}$. Here $B^*$ stands for the unit coball bundle and $\theta$ is a certain characteristic class depending on the principal symbol of the Fourier integral operator. In the special case when X=Y we obtain a different proof of the theorem of Epstein and Melrose.

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