Legendrian surgery

TL;DR

This paper provides an overview of Eliashberg's Legendrian surgery method, connecting it to wrapped Floer cohomology and holomorphic curve theories, and discusses its applications to invariants of singular Legendrians and Lagrangians.

Contribution

It offers a comprehensive overview of Legendrian surgery techniques and their role in understanding holomorphic curve invariants and algebraic structures in symplectic topology.

Findings

Clarifies the relations between holomorphic curve theories via Legendrian surgery

Demonstrates applications to invariants of singular Legendrians and Lagrangians

Provides a unified perspective on algebraic constructions in symplectic topology

Abstract

This is an overview paper that describes Eliashberg's Legendrian surgery approach to wrapped Floer cohomology and use it to derive the basic relations between various holomorphic curve theories with additional algebraic constructions. We also give a brief discussion of further results that use the surgery perspective, e.g., for holomorphic curve invariants of singular Legendrians and Lagrangians.