Semi-global Kuranishi charts and the definition of contact homology

Abstract

We define the contact homology algebra for any contact manifold and show that it is an invariant of the contact manifold. More precisely, given a contact manifold $(M,\xi )$ and some auxiliary data $\mathcal{D}$, we define an algebra $HC(\mathcal{D})$. If ${\mathcal{D}}_1$ and ${\mathcal{D}}_2$ are two choices of auxiliary data for $(M,\xi )$, then $HC({\mathcal{D}}_1)$ and $HC({\mathcal{D}}_2)$ are isomorphic. We use a simplified version of Kuranishi perturbation theory, consisting of semi-global Kuranishi charts.

arXiv commentfixed a latex error for index of notations

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• $S^1$-equivariant symplectic homology and linearized contact homology
• Symplectic and contact differential graded algebras
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• Automatic transversality in contact homology II: filtrations and computations
• Lectures on Polyfolds and Symplectic Field Theory
• On the embedding complexity of Liouville manifolds
• Cobordism maps in embedded contact homology
• Combinatorial Reeb dynamics on punctured contact 3-manifolds
• S^1-equivariant contact homology for hypertight contact forms
• Higher Symplectic Capacities and the Stabilized Embedding Problem for Integral Ellipsoids
• Foliations, contact structures and their interactions in dimension three
• Simplified SFT moduli spaces for Legendrian links