Journal of Symplectic Geometry

Volume 14 (2016)

Number 4

Cylindrical contact homology for dynamically convex contact forms in three dimensions

Pages: 983 – 1012



Michael Hutchings (Department of Mathematics, University of California at Berkeley)

Jo Nelson (School of Mathematics, Institute for Advanced Study, Princeton, New Jersey, U.S.A.)


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.

Published 10 January 2017