Symplectic homology product via Legendrian surgery

TL;DR

This paper advances the understanding of symplectic homology by explicitly describing its product and BV-operator in terms of Legendrian surgery, building on prior work relating symplectic and Legendrian homologies.

Contribution

It provides a new explicit description of the symplectic homology product and BV-operator using Legendrian surgery techniques, extending previous results on symplectic homology as a vector space.

Findings

Explicit formulas for the symplectic homology product

Description of the BV-operator in the Legendrian context

Extension of previous homology algebra relations

Abstract

This research announcement continues the study of the symplectic homology of Weinstein manifolds undertaken in [BEE1] where the symplectic homology, as a vector space, was expressed in terms of the Legendrian homology algebra of the attaching spheres of critical handles. Here we express the product and $\BV$-operator of symplectic homology in that context.