Microlocal theory of sheaves and Tamarkin's non displaceability theorem

TL;DR

This paper explores Tamarkin's microlocal sheaf theory approach to symplectic non-displaceability, offering new insights, notions, and results that deepen understanding of Tamarkin's theorems.

Contribution

It provides alternative proofs, introduces new concepts, and presents novel results in the microlocal sheaf theory framework for symplectic geometry.

Findings

New notions in microlocal sheaf theory

Alternative proofs of Tamarkin's theorems

Additional results on non-displaceability

Abstract

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.