2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77252An index formula is proposed for contact transformations between contact manifolds equipped with CR structures or with fillings by symplectic manifolds. The formula generalizes the Atiyah-Singer formula and gives a conjectured formula for the index of Fourier integral operators, as well as Epstein's relative index for CR structures.This is an expanded version of a lecture given at the Symposium on Geometric Methods in Asymptotic Analysis, RIMS, Kyoto, May 20, 1997Differential GeometrySymplectic Geometry58G10text