Abstract
Let be an open interval containing zero, let be a real manifold, let be its cotangent bundle with the zero-section removed, and let be a homogeneous Hamiltonian isotopy of with . Let be the conic Lagrangian submanifold associated with . We prove the existence and unicity of a sheaf on whose microsupport is contained in the union of and the zero-section and whose restriction to is the constant sheaf on the diagonal of . We give applications of this result to problems of nondisplaceability in contact and symplectic topology. In particular we prove that some strong Morse inequalities are stable by Hamiltonian isotopies, and we also give results of nondisplaceability for nonnegative isotopies in the contact setting.
Citation
Stéphane Guillermou. Masaki Kashiwara. Pierre Schapira. "Sheaf quantization of Hamiltonian isotopies and applications to nondisplaceability problems." Duke Math. J. 161 (2) 201 - 245, 1 February 2012. https://doi.org/10.1215/00127094-1507367
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