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.

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References in corpus (4)

• Relative asymptotic behavior of pseudoholomorphic half-cylinders
• Contact homology and virtual fundamental cycles
• Symplectic and contact differential graded algebras
• Automatic Transversality and Orbifolds of Punctured Holomorphic Curves in Dimension Four

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• Automatic transversality in contact homology II: filtrations and computations
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• 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