An exact sequence for contact- and symplectic homology

DOI10.1007/s00222-008-0159-1zbMath1167.53071arXiv0704.2169OpenAlexW2040738246MaRDI QIDQ1006878

Alexandru Oancea, Frédéric Bourgeois

Publication date: 26 March 2009

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0704.2169

zbMATH Keywords

symplectic homologycontact homology

Mathematics Subject Classification ID

Symplectic aspects of Floer homology and cohomology (53D40)

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Cites Work

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• The Künneth formula in Floer homology for manifolds with restricted contact type boundary
• Floer homology and the heat flow
• Symplectic hypersurfaces and transversality in Gromov-Witten theory
• Fibered symplectic cohomology and the Leray-Serre spectral sequence
• A general Fredholm theory. III: Fredholm functors and polyfolds
• A general Fredholm theory. II: Implicit function theorems
• The Maslov index for paths
• Symplectic homology. I: Open sets in \(\mathbb{C}^ n\)
• Compactness results in symplectic field theory
• Lagrangian embeddings into subcritical Stein manifolds
• Handle attaching in symplectic homology and the chord conjecture
• Properties of pseudoholomorphic curves in symplectisations. I: Asymptotics
• Coherent orientations in symplectic field theory
• Cylindrical contact homology of subcritical Stein-fillable contact manifolds
• Functors and computations in Floer homology with applications. I
• Applications of symplectic homology. II: Stability of the action spectrum
• Symplectic homology, autonomous Hamiltonians, and Morse-Bott moduli spaces
• THE GYSIN EXACT SEQUENCE FOR S¹-EQUIVARIANT SYMPLECTIC HOMOLOGY
• Rabinowitz Floer homology and symplectic homology
• On the Floer homology of cotangent bundles
• The role of string topology in symplectic field theory
• Morse theory for periodic solutions of hamiltonian systems and the maslov index
• Fredholm theory and transversality for noncompact pseudoholomorphic mapsin symplectizations
• Symplectic homology product via Legendrian surgery
• Lagrangian barriers and symplectic embeddings

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