Symplectic homology product via Legendrian surgery

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.

30 pages, 4 figures. v2: a number of typos were corrected. v3: corrected sign error in Equation (2.4)

References in corpus (2)

• Symplectic homology product via Legendrian surgery
• Rational Symplectic Field Theory over Z_2 for exact Lagrangian cobordisms

Cited by in corpus (15)

• Symplectic cohomology and duality for the wrapped Fukaya category
• Symplectic homology and the Eilenberg-Steenrod axioms
• A complete knot invariant from contact homology
• Koszul duality patterns in Floer theory
• Legendrian Fronts for Affine Varieties
• Knot contact homology
• Symplectic homology product via Legendrian surgery
• Symplectic Homology of complements of smooth divisors
• Fukaya Categories as Categorical Morse Homology
• Holomorphic curves for Legendrian surgery
• Orientations of Morse flow trees in Legendrian contact homology
• Calabi-Yau structure on the Chekanov-Eliashberg algebra of a Legendrian sphere
• Cyclic Homology of Fukaya Categories and the Linearized Contact Homology
• Legendrian contact homology in the product of a punctured Riemann surface and the real line
• Simplified SFT moduli spaces for Legendrian links