Symplectic homology

General Introduction
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Online References
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
arXiv:1003.1781 Topological quantum field theory structure on symplectic cohomology from arXiv Front: math.AT by Alexander F. Ritter We construct the TQFT structures on symplectic cohomology and wrapped Floer cohomology, and their twisted analogues. The TQFT respects the isomorphism between the symplectic cohomology of a cotangent bundle and the homology of the free loop space: it recovers the TQFT of string topology. We also prove the TQFT respects Viterbo restriction maps and the canonical maps from ordinary cohomology. Then we construct the module structure of wrapped Floer cohomology over symplectic cohomology. Finally we prove that symplectic cohomology vanishes iff Rabinowitz Floer cohomology vanishes. We obtain applications to the symplectic topology of exact Lagrangian submanifolds and contact hypersurfaces. The module structure of wrapped Floer cohomology yields applications to the Arnol'd chord conjecture. If the boundary of a Liouville domain is Hamiltonian displaceable in the symplectization then the symplectic cohomology vanishes and there are no exact Lagrangians.
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