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

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