HF=HM. II: Reeb orbits and holomorphic curves for the ech/Heegaard Floer correspondence

DOI10.2140/gt.2020.24.2855zbMath1494.57056arXiv1008.1595OpenAlexW3118546772MaRDI QIDQ2224542

Clifford Henry Taubes, Çağatay Kutluhan, Yi-Jen Lee

Publication date: 4 February 2021

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.1595

zbMATH Keywords

Heegaard Floer homologySeiberg-Witten Floer homology

Mathematics Subject Classification ID

Applications of global analysis to structures on manifolds (57R57) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Floer homology (57R58) Invariants of 3-manifolds (including skein modules, character varieties) (57K31)

Related Items (21)

A Survey of the Thurston Norm ⋮ Bordered Floer homology and a meridional class of knot ⋮ Admissible transverse surgery does not preserve tightness ⋮ Notes on Bordered Floer Homology ⋮ Lecture Notes on Embedded Contact Homology ⋮ Instanton Floer homology, sutures, and Euler characteristics ⋮ Equivariant Seiberg-Witten-Floer cohomology ⋮ A survey of the homology cobordism group ⋮ On the Frøyshov invariant and monopole Lefschetz number ⋮ Seiberg-Witten Floer spectra and contact structures ⋮ HF=HM. I: Heegaard Floer homology and Seiberg-Witten Floer homology ⋮ HF=HM. III: Holomorphic curves and the differential for the ech/Heegaard Floer correspondence ⋮ HF=HM. IV: The Seiberg-Witten Floer homology and ech correspondence ⋮ HF=HM. V: Seiberg-Witten Floer homology and handle additions ⋮ Comparing homological invariants for mapping classes of surfaces ⋮ An exposition of the equivalence of Heegaard Floer homology and embedded contact homology ⋮ On the equivalence of contact invariants in sutured Floer homology theories ⋮ On the monopole Lefschetz number of finite-order diffeomorphisms ⋮ Bordered Floer homology and incompressible surfaces ⋮ The groups of diffeomorphisms and homeomorphisms of 4-manifolds with boundary ⋮ Floer theory and its topological applications

Cites Work

• Embedded contact homology and Seiberg-Witten Floer cohomology. IV.
• Tamed to compatible: symplectic forms via moduli space integration
• A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order
• Multiple integrals in the calculus of variations
• Gluing pseudoholomorphic curves along branched covered cylinders. II.
• Pseudo holomorphic curves in symplectic manifolds
• Gromov's compactness of pseudo-holomorphic curves and symplectic geometry
• The local behaviour of holomorphic curves in almost complex 4-manifolds
• Torsion invariants of Spin\(^c\)-structures on 3-manifolds
• Holomorphic disks and topological invariants for closed three-manifolds
• A compendium of pseudoholomorphic beasts in \({\mathbf R}\times (S^1\times S^2)\)
• Properties of pseudoholomorphic curves in symplectisations. I: Asymptotics
• An index inequality for embedded pseudoholomorphic curves in symplectizations
• HF=HM. I: Heegaard Floer homology and Seiberg-Witten Floer homology
• HF=HM. III: Holomorphic curves and the differential for the ech/Heegaard Floer correspondence
• Rounding corners of polygons and the embedded contact homology of \(T^3\)
• Pseudoholomorphic punctured spheres in \(\mathbb R\times(S^1\times S^2)\): properties and existence
• A cylindrical reformulation of Heegaard Floer homology
• Relative asymptotic behavior of pseudoholomorphic half-cylinders
• Gromov's Compactness Theorem for Pseudo Holomorphic Curves
• SW ⇒ Gr: From the Seiberg-Witten equations to pseudo-holomorphic curves

This page was built for publication: HF=HM. II: Reeb orbits and holomorphic curves for the ech/Heegaard Floer correspondence