Holomorphic curves for Legendrian surgery

Abstract

Let $X$ be a Weinstein manifold with ideal contact boundary $Y$. If $\Lambda \subset Y$ is a link of Legendrian spheres in $Y$ then by attaching Weinstein handles to $X$ along $\Lambda$ we get a Weinstein cobordism $X_{\Lambda }$ with a collection of Lagrangian co-core disks $C$ corresponding to $\Lambda$. In \cite{BEE, EL} it was shown that the wrapped Floer cohomology $C{W}^{\ast }(C)$ of $C$ in the Weinstein manifold $X_{\Lambda }^{\prime }=X\cup X_{\Lambda }$is naturally isomorphic to the Legendrian differential graded algebra $C{E}^{\ast }(\Lambda )$ of $\Lambda$ in $Y$. The argument uses properties of moduli spaces of holomorphic curves, the proofs of which were only sketched. The purpose of this paper is to provide proofs of these properties.

36 pages, 5 figures

References in corpus (4)

• Compactness results in Symplectic Field Theory
• Duality between Lagrangian and Legendrian invariants
• Symplectic and contact differential graded algebras
• Symplectic homology product via Legendrian surgery

Cited by in corpus (11)

• Homological mirror symmetry for Milnor fibers of simple singularities
• Sheaves via augmentations of Legendrian surfaces
• Fiber Floer cohomology and conormal stops
• An introduction to Weinstein handlebodies for complements of smoothed toric divisors
• Geometric and algebraic presentations of Weinstein domains
• Combinatorial Reeb dynamics on punctured contact 3-manifolds
• The persistence of a relative Rabinowitz-Floer complex
• Legendrian contact homology for attaching links in higher dimensional subcritical Weinstein manifolds
• Localization and flexibilization in symplectic geometry
• Homological invariants of codimension 2 contact submanifolds
• Lagrangian cobordism functor in microlocal sheaf theory I