Journal of Symplectic Geometry
Volume 14 (2016)
Cylindrical contact homology for dynamically convex contact forms in three dimensions
Pages: 983 – 1012
We show that for dynamically convex contact forms in three dimensions, the cylindrical contact homology differential $\partial$ 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 $\partial^2 = 0$. 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.