Effect of Legendrian Surgery

TL;DR

This paper summarizes results on symplectic invariants of Weinstein manifolds, providing examples, applications, and sketching proofs, with implications for Seidel's conjecture relating symplectic and Hochschild homology.

Contribution

It introduces new computations of symplectic invariants and demonstrates their implications for a major conjecture in symplectic topology.

Findings

Results imply Seidel's conjecture relating symplectic and Hochschild homology.

Provides new examples and applications of Weinstein manifold invariants.

Sketches proofs for the computed invariants.

Abstract

The paper is a summary of the results of the authors concerning computations of symplectic invariants of Weinstein manifolds and contains some examples and applications. Proofs are sketched. The detailed proofs will appear in our forthcoming paper. In the Appendix written by S. Ganatra and M. Maydanskiy it is shown that the results of this paper imply P. Seidel's conjecture equating symplectic homology with Hochschild homology of a certain Fukaya category.