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arXiv · 1407.2898

Cylindrical contact homology for dynamically convex contact forms in three dimensions

Michael Hutchings·Jo Nelson
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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.

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Michael Hutchings, Jo Nelson. 2014-07-10. Cylindrical contact homology for dynamically convex contact forms in three dimensions. https://arxiv.org/abs/1407.2898

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