Cylindrical contact homology for dynamically convex contact forms in three dimensions

Abstract

We show that for dynamically convex contact forms in three dimensions, the cylindrical contact homology differential d can be defined by directly counting holomorphic cylinders for a generic almost complex structure, without any abstract perturbation of the Cauchy-Riemann equation. We also prove that d^2 = 0. Invariance of cylindrical contact homology in this case can be proved using S^1-dependent almost complex structures, similarly to work of Bourgeois-Oancea; this will be explained in another paper.

v3: corrected Lemma 2.5(b), to appear in Journal of Symplectic Geometry

References in corpus (1)

• $S^1$-equivariant symplectic homology and linearized contact homology

Cited by in corpus (4)

• Contact homology and virtual fundamental cycles
• Semi-global Kuranishi charts and the definition of contact homology
• On the stabilized symplectic embedding problem for ellipsoids
• Automatic transversality in contact homology I: Regularity