Holomorphic curves in the presence of holomorphic hypersurface foliations

Abstract

We prove a result which establishes restrictions on the pseudoholomorphic curves which can exist in a stable Hamiltonian manifold in the presence of certain $\mathbb{R}$-invariant foliations of the symplectization by holomorphic hypersurfaces. This result has applications in the first author's work on algebraic torsion in higher dimensional contact manifolds.

14 pages; adapted from Appendix C of arXiv:1711.01562 (the first author's PhD thesis)

References in corpus (5)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Relative asymptotic behavior of pseudoholomorphic half-cylinders
• Intersection theory of punctured pseudoholomorphic curves
• On symplectic fillings of spinal open book decompositions I: Geometric constructions
• Algebraic Torsion in higher-dimensional contact manifolds

Cited by in corpus (4)

• Higher symplectic capacities
• Counting curves with local tangency constraints
• Symplectic capacities, unperturbed curves, and convex toric domains
• Homological invariants of codimension 2 contact submanifolds