# Sheaves and symplectic geometry of cotangent bundles

## TL;DR

This paper consolidates and simplifies existing microlocal sheaf theory results to explore symplectic geometry of cotangent bundles, recovering key theorems and proving new conjectures.

## Contribution

It unifies previous preprints with simplified proofs and applies microlocal sheaf theory to derive fundamental symplectic geometry results and solve a three cusps conjecture.

## Key findings

- Recovered Gromov nonsqueezing theorem
- Established Gromov-Eliashberg rigidity
- Proved a three cusps conjecture

## Abstract

This paper is essentially made of the three preprints arXiv:1212.5818, arXiv:1311.0187, arXiv:1603.07876 gathered in a single text, with simplified proofs. We recall several results of the microlocal theory of sheaves of Kashiwara-Schapira and apply them to study the symplectic geometry of cotangent bundles. We explain how we can recover the Gromov nonsqueezing theorem, the Gromov-Eliashberg rigidity theorem, the existence of graph selectors, we prove a three cusps conjecture about curves on the sphere and we recover more recent results on the topology of exact Lagrangian submanifolds of cotangent bundles.

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Source: https://tomesphere.com/paper/1905.07341