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Microlocal theory of sheaves and Tamarkin’s non displaceability theorem. (English) Zbl 1319.32006
Castano-Bernard, Ricardo (ed.) et al., Homological mirror symmetry and tropical geometry. Based on the workshop on mirror symmetry and tropical geometry, Cetraro, Italy, July 2–8, 2011. Cham: Springer (ISBN 978-3-319-06513-7/pbk; 978-3-319-06514-4/ebook). Lecture Notes of the Unione Matematica Italiana 15, 43-85 (2014).
Summary: This paper is an attempt to better understand Tamarkin’s approach of classical non-displaceability theorems of symplectic geometry, based on the microlocal theory of sheaves, a theory whose main features we recall here. If the main theorems are due to Tamarkin, our proofs may be rather different and in the course of the paper we introduce some new notions and obtain new results which may be of interest.
For the entire collection see [Zbl 1300.14001].

MSC:
32C38 Sheaves of differential operators and their modules, \(D\)-modules
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
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