Microlocal theory of sheaves and symplectic geometry II

The microsupport of a sheaf on a manifold, introduced by Kashiwara and Schapira, is a subset of the cotangent bundle of the manifold which says whether the group of sections of the sheaf over an open set is modified when we deform the open set. For a given homogeneous symplectic transformation of the cotangent bundle we show under some hypothesis that there exists a sheaf whose microsupport is the graph of the transformation. We deduce some (already known) versions of Arnold's conjectures about the “non-displaceability” of some subsets of the cotangent bundle. In the talk I will recall some aspects of sheaf theory and give an illustration of the above result.