HF=HM. IV: The Seiberg-Witten Floer homology and ech correspondence

DOI10.2140/gt.2020.24.3219zbMath1494.57058arXiv1107.2297OpenAlexW1817415616MaRDI QIDQ2224544

Çağatay Kutluhan, Yi-Jen Lee, Clifford Henry Taubes

Publication date: 4 February 2021

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

Full work available at URL: https://arxiv.org/abs/1107.2297

zbMATH Keywords

Heegaard Floer homologypseudoholomorphic curvesSeiberg-Witten Floer homology

Mathematics Subject Classification ID

Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) Applications of global analysis to structures on manifolds (57R57) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Floer homology (57R58) Invariants of 3-manifolds (including skein modules, character varieties) (57K31)

Related Items (15)

A Survey of the Thurston Norm ⋮ Bordered Floer homology and a meridional class of knot ⋮ 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. 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

Cites Work

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• The Weinstein conjecture for stable Hamiltonian structures
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• Compactness results in symplectic field theory
• \(\text{Gr}\Rightarrow\text{SW}\): from pseudo-holomorphic curves to Seiberg-Witten solutions.
• Holomorphic disks and topological invariants for closed three-manifolds
• HF=HM. I: Heegaard Floer homology and Seiberg-Witten Floer homology
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• HF=HM. III: Holomorphic curves and the differential for the ech/Heegaard Floer correspondence
• The Seiberg-Witten equations and the Weinstein conjecture
• Asymptotic spectral flow for Dirac operators
• Rounding corners of polygons and the embedded contact homology of \(T^3\)
• SW ⇒ Gr: From the Seiberg-Witten equations to pseudo-holomorphic curves
• Taubes’s proof of the Weinstein conjecture in dimension three

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