Completeness of derived interleaving distances and sheaf quantization of non-smooth objects
arXiv:2201.02598 · doi:10.1007/s00208-024-02815-x
Abstract
We develop sheaf-theoretic methods to deal with non-smooth objects in symplectic geometry. We show the completeness of a derived category of sheaves with respect to the interleaving distance and construct a sheaf quantization of a Hamiltonian homeomorphism. We also develop Lusternik--Schnirelmann theory in the microlocal theory of sheaves. With these new sheaf-theoretic methods, we prove an Arnold-type theorem for the image of a compact exact Lagrangian submanifold under a Hamiltonian homeomorphism.
arXiv comment41 pages, 1 figure. v4: Final version, published in Math. Ann
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