导出交错距离的完备性与非光滑对象的层量子化
Completeness of derived interleaving distances and sheaf quantization of non-smooth objects
AI总结：
本研究开发层论方法处理辛几何非光滑对象，证明层导出范畴交错距离完备性、构造哈密顿同胚层量子化，发展微局部层论的Lusternik--Schnirelmann理论，证明紧恰当拉格朗日子流形哈密顿同胚像的Arnold型定理。
摘要：
我们开发了层论方法来处理辛几何中的非光滑对象。我们证明了层的导出范畴关于交错距离的完备性，并构造了哈密顿同胚的层量子化。我们还在层的微局部理论中发展了Lusternik--Schnirelmann理论。借助这些新的层论方法，我们证明了紧恰当拉格朗日子流形在哈密顿同胚下的像的Arnold型定理。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
