An overview of knot Floer homology
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Publication:5136623
DOI10.1090/pspum/099/01742zbMath1448.57015arXiv1706.07729OpenAlexW2964187767MaRDI QIDQ5136623
Zoltán Szabó, Peter S. Ozsváth
Publication date: 27 November 2020
Published in: Proceedings of Symposia in Pure Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1706.07729
Symplectic aspects of Floer homology and cohomology (53D40) Floer homology (57R58) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02) Higher-dimensional knots and links (57K45) Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.) (57K18)
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Cites Work
- Combinatorial proofs in bordered Heegaard Floer homology
- Computing \(\widehat {HF}\) by factoring mapping
- Nonorientable slice genus can be arbitrarily large
- Notes on the knot concordance invariant upsilon
- Combinatorial tangle Floer homology
- On manifolds homeomorphic to \({\mathbb{C}}P^ 2\#8\overline{{\mathbb{C}}P}^ 2\)
- Khovanov homology and the slice genus
- Knot Floer homology and rational surgeries
- A link surgery spectral sequence in monopole Floer homology
- Khovanov homology is an unknot-detector
- Heegaard Floer homology as morphism spaces
- Irreducible 4-manifolds need not be complex
- Polynomial invariants for smooth four-manifolds
- Lagrangian boundary conditions for anti-self-dual instantons and the Atiyah-Floer conjecture
- Holomorphic discs and sutured manifolds
- Casson's invariant and gauge theory
- Holomorphic disks, link invariants and the multi-variable Alexander polynomial
- Fukaya categories and Picard-Lefschetz theory
- An algorithm for computing some Heegaard Floer homologies
- The sutured Floer homology polytope
- Knots, sutures, and excision
- Man and machine thinking about the smooth 4-dimensional Poincaré conjecture
- Transverse knots distinguished by knot Floer homology
- Pseudo holomorphic curves in symplectic manifolds
- Irrationality and the h-cobordism conjecture
- Definite 4-manifolds
- Applications of Donaldson's theorems to classical knot concordance, homology 3-spheres and property P
- Morse theory for Lagrangian intersections
- Invariants in contact topology
- Simply-connected irreducible 4-manifolds with no symplectic structures
- Arbitrary N-vortex solutions to the first order Ginzburg-Landau equations
- A generalized bridge number for links in 3-manifolds
- Gauge theory for embedded surfaces. I
- Self-dual instantons and holomorphic curves
- Scalar curvature and the Thurston norm
- Knot Floer homology and the four-ball genus
- Heegaard Floer homology and alternating knots
- Seiberg-Witten Floer stable homotopy type of three-manifolds with \(b_1=0\)
- On Khovanov's categorification of the Jones polynomial
- Lefschetz pencils on symplectic manifolds.
- Kauffman states, bordered algebras, and a bigraded knot invariant
- Holomorphic disks and topological invariants for closed three-manifolds
- The Seiberg-Witten equations and four-manifolds with boundary
- An instanton-invariant for 3-manifolds
- An application of gauge theory to four dimensional topology
- Equivariant Seiberg-Witten Floer homology
- Floer homology of surgeries on two-bridge knots
- On symplectic fillings
- Holomorphic triangle invariants and the topology of symplectic four-manifolds
- Holomorphic disks and knot invariants
- Holomorphic disks and genus bounds
- Computations of the Ozsvath-Szabo knot concordance invariant
- Embedding knots and links in an open book. I: Basic properties
- Monopoles and four-manifolds
- The Seiberg-Witten invariants and symplectic forms
- Embedded surfaces and the structure of Donaldson's polynomial invariants
- More constraints on symplectic forms from Seiberg-Witten invariants
- Transversality in elliptic Morse theory for the symplectic action
- The lens space realization problem
- A categorification of the Jones polynomial
- On the Upsilon invariant of cable knots
- HF=HM. I: Heegaard Floer homology and Seiberg-Witten Floer homology
- On the upsilon invariant and satellite knots
- Bordered knot algebras with matchings
- Correction to the article ``An infinite-rank summand of topologically slice knots
- Bimodules in bordered Heegaard Floer homology
- Concordance homomorphisms from knot Floer homology
- A combinatorial description of knot Floer homology
- Grid diagrams and the Ozsváth-Szabó tau-invariant
- Khovanov-Seidel quiver algebras and Ozsváth-Szabó's bordered theory
- Legendrian knots, transverse knots and combinatorial Floer homology
- On combinatorial link Floer homology
- Knot Floer homology detects fibred knots
- Knot Floer homology and integer surgeries
- A cylindrical reformulation of Heegaard Floer homology
- Invariants of knot cobordism
- On knot Floer homology and lens space surgeries
- Knot Floer homology of \((1,1)\)-knots
- An endomorphism of the Khovanov invariant
- Monopoles and lens space surgeries
- Quivers, Floer cohomology, and braid group actions
- COMPUTATIONS OF HEEGAARD-FLOER KNOT HOMOLOGY
- Knot Floer homology detects genus-one fibred knots
- Morse Theory. (AM-51)
- Parameterizations of 1-Bridge Torus Knots
- Unoriented Knot Floer Homology and the Unoriented Four-Ball Genus
- Bordered Heegaard Floer homology
- The Spectral Flow and the Maslov Index
- Homological Algebra of Mirror Symmetry
- The Seiberg-Witten equations and 4-manifold topology
- Tour of bordered Floer theory
- Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions
- Matrix factorizations and link homology
- Arc-presentations of links: Monotonic simplification
- Singular Points of Complex Hypersurfaces. (AM-61)
- SW ⇒ Gr: From the Seiberg-Witten equations to pseudo-holomorphic curves
- Homotopy Associativity of H-Spaces. I
- Hamiltonian handleslides for Heegaard Floer homology
- On the Khovanov and knot Floer homologies of quasi-alternating links
- Foliations and the topology of 3-manifolds
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