Cylindrical contact homology for dynamically convex contact forms in three dimensions

By Michael Hutchings, J. Nelson. 2014

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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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/39afd46af59552bb91e24456d0a80709ef303a09