Contact homology and virtual fundamental cycles

Abstract

We give a construction of contact homology in the sense of Eliashberg--Givental--Hofer. Specifically, we construct coherent virtual fundamental cycles on the relevant compactified moduli spaces of pseudo-holomorphic curves.

Final version to appear in JAMS, 102 pages, 10 figures

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Cited by in corpus (33)

• Floer theory for Lagrangian cobordisms
• Semi-global Kuranishi charts and the definition of contact homology
• Maximal contact and symplectic structures
• String topology with gravitational descendants, and periods of Landau-Ginzburg potentials
• Mayer-Vietoris property for relative symplectic cohomology
• Counting curves with local tangency constraints
• Symplectic fillings of asymptotically dynamically convex manifolds I
• Automatic transversality in contact homology II: filtrations and computations
• Symplectic capacities, unperturbed curves, and convex toric domains
• Lectures on Polyfolds and Symplectic Field Theory
• Morse-Bott cohomology from homological perturbation theory
• On the embedding complexity of Liouville manifolds
• On properties of Bourgeois contact structures
• Combinatorial Reeb dynamics on punctured contact 3-manifolds
• On the stabilized symplectic embedding problem for ellipsoids
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• Polyfold and SFT Notes II: Local-Local M-Polyfold Constructions
• Polyfold and SFT Notes I: A Primer on Polyfolds and Construction Tools
• The persistence of a relative Rabinowitz-Floer complex
• Multiplicity of Closed Reeb Orbits on Prequantization Bundles
• A characterization of heaviness in terms of relative symplectic cohomology
• Higher Symplectic Capacities and the Stabilized Embedding Problem for Integral Ellipsoids
• Exact orbifold fillings of contact manifolds
• Lattice Formulas For Rational SFT Capacities
• Dynamical Quantization of Contact Structures
• Homological invariants of codimension 2 contact submanifolds
• Essential tori in spaces of symplectic embeddings
• Foliations, contact structures and their interactions in dimension three
• Connected sums of Brieskorn contact $5$-spheres
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• A landscape of contact manifolds via rational SFT
• A-infinity category of Lagrangian cobordisms in the symplectization of PxR