Completeness of derived interleaving distances and sheaf quantization of non-smooth objects
Symplectic Geometry
2024-03-14 v4 Algebraic Topology
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.
Cite
@article{arxiv.2201.02598,
title = {Completeness of derived interleaving distances and sheaf quantization of non-smooth objects},
author = {Tomohiro Asano and Yuichi Ike},
journal= {arXiv preprint arXiv:2201.02598},
year = {2024}
}
Comments
41 pages, 1 figure. v4: Final version, published in Math. Ann