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## Search Articles

2015, Mathematical surveys and monographs, ISBN 9781470417376, Volume no. 208., x, 410

Differential geometry -- Symplectic geometry, contact geometry -- Contact manifolds, general | Homology theory | Knot theory | Manifolds and cell complexes -- Low-dimensional topology -- Invariants of knots and 3-manifolds | Link theory | Manifolds and cell complexes -- Differential topology -- Floer homology

Book

2011, 1st pbk. ed., New mathematical monographs, ISBN 9780521184762, Volume 10, xii, 796

This work provides a comprehensive treatment of Floer homology, based on the Seiberg-Witten monopole equations.

Homology theory | Seiberg-Witten invariants | Moduli theory | Three-manifolds (Topology)

Homology theory | Seiberg-Witten invariants | Moduli theory | Three-manifolds (Topology)

Book

2016, Volume 680.

Quantum theory -- Quantum field theory; related classical field theories -- Topological field theories | Link theory | Quantum theory -- Quantum field theory; related classical field theories -- String and superstring theories; other extended objects (e.g., branes) | Homology theory | Knot theory | Manifolds and cell complexes -- Low-dimensional topology -- Invariants of knots and 3-manifolds | Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Quantum groups (quantized enveloping algebras) and related deformations | Manifolds and cell complexes -- Differential topology -- Floer homology | Curves

Conference Proceeding

2013, Universitext, ISBN 9781447154952, 595

...: the 'Arnold conjecture'. Presents building blocks of Floer homology and more.

Morse theory | Floer homology

Morse theory | Floer homology

eBook

Quantum topology, ISSN 1663-487X, 2018, Volume 9, Issue 1, pp. 1 - 37

We use Heegaard Floer homology with twisted coefficients to define numerical invariants for arbitrary closed 3-manifolds equipped torsion spin(c...

Heegaard floer homology | Intersection forms | Smooth 4-manifolds | Correction terms | Quantum Science & Technology | Physical Sciences | Mathematics | Physics | Science & Technology

Heegaard floer homology | Intersection forms | Smooth 4-manifolds | Correction terms | Quantum Science & Technology | Physical Sciences | Mathematics | Physics | Science & Technology

Journal Article

Commentarii Mathematici Helvetici, ISSN 0010-2571, 2018, Volume 93, Issue 3, pp. 587 - 644

We construct connections on $S^1$-equivariant Hamiltonian Floer cohomology, which differentiate with respect to certain formal parameters.

Algebraic topology | Differential geometry | Manifolds and cell complexes | Floer homology | Gauss–Manin connection | Topological quantum field theory | Physical Sciences | Mathematics | Science & Technology

Algebraic topology | Differential geometry | Manifolds and cell complexes | Floer homology | Gauss–Manin connection | Topological quantum field theory | Physical Sciences | Mathematics | Science & Technology

Journal Article

1995, Progress in mathematics, ISBN 081765044X, Volume 133., xii, 685

Book

2014, Universitext, ISBN 9781447154952

eBook

Quantum topology, ISSN 1663-487X, 2018, Volume 9, Issue 2, pp. 207 - 228

In joint work with Yang Huang, we defined a canonical absolute grading on Heegaard Floer homology by homotopy classes of oriented 2-plane fields...

Embedded contact homology | Heegaard Floer homology | Absolute gradings | Quantum Science & Technology | Physical Sciences | Mathematics | Physics | Science & Technology

Embedded contact homology | Heegaard Floer homology | Absolute gradings | Quantum Science & Technology | Physical Sciences | Mathematics | Physics | Science & Technology

Journal Article

Quantum topology, ISSN 1663-487X, 2018, Volume 9, Issue 2, pp. 349 - 418

....
For generic holonomy perturbations pi, the traceless SU(2) character variety R-pi(Y, L) of an n-stranded tangle L in a homology 3-ball Y is stratified with a finite singular stratum and top stratum a smooth manifold...

Holonomy perturbation | Floer homology | Character variety | Hamiltonian twist flow | Quantum Science & Technology | Physical Sciences | Mathematics | Physics | Science & Technology

Holonomy perturbation | Floer homology | Character variety | Hamiltonian twist flow | Quantum Science & Technology | Physical Sciences | Mathematics | Physics | Science & Technology

Journal Article

2004, Kluwer texts in the mathematical sciences, ISBN 1402026951, Volume 29, vii, 324

Book

American journal of mathematics, ISSN 0002-9327, 8/2009, Volume 131, Issue 4, pp. 1047 - 1063

Given a closed 3-manifold Y, we show that the Heegaard Floer homology determines whether Y fibres over the circle with a fibre of negative Euler characteristic...

Mathematical manifolds | Mathematical theorems | Topological theorems | Critical points | Polynomials | Mathematical surfaces | Mathematical rings | Coefficients | Closed curves | Homology theory | Three-manifolds (Topology) | Physical Sciences | Mathematics | Science & Technology | Manifolds (Mathematics) | Research | Geometry | Eulers equations | Theorems | Topological manifolds

Mathematical manifolds | Mathematical theorems | Topological theorems | Critical points | Polynomials | Mathematical surfaces | Mathematical rings | Coefficients | Closed curves | Homology theory | Three-manifolds (Topology) | Physical Sciences | Mathematics | Science & Technology | Manifolds (Mathematics) | Research | Geometry | Eulers equations | Theorems | Topological manifolds

Journal Article

Quantum topology, ISSN 1663-487X, 09/2015, Volume 6, Issue 3, pp. 475 - 513

Quantum Topol. 6 (2015), no. 3, 475-513 O. Plamenevskaya associated to each transverse knot K an element of the
Khovanov homology of K...

Khovanov homology | Flype | Khovanov spectrum | Transverse knot | Mathematics - Geometric Topology

Khovanov homology | Flype | Khovanov spectrum | Transverse knot | Mathematics - Geometric Topology

Journal Article

Commentarii Mathematici Helvetici, ISSN 0010-2571, 2012, Volume 87, Issue 1, pp. 41 - 69

...)$, what can be said about the symplectically aspherical manifolds $(W, \omega)$ bounded by $(\Sigma, \xi)$? We first extend a theorem of Eliashberg, Floer and McDuff to prove that, under suitable assumptions, the map...

Several complex variables and analytic spaces | General | Differential geometry | Manifolds and cell complexes | Obstructions to contact embeddings | Topology of symplectic fillings of contact manifolds | Physical Sciences | Mathematics | Science & Technology | Symplectic Geometry

Several complex variables and analytic spaces | General | Differential geometry | Manifolds and cell complexes | Obstructions to contact embeddings | Topology of symplectic fillings of contact manifolds | Physical Sciences | Mathematics | Science & Technology | Symplectic Geometry

Journal Article

2007, Universitext, ISBN 0387495096, xiv, 241

This text aims to give the reader a taste of the 'unreasonable effectiveness' of Morse theory.

Morse theory | Calculus of variations

Morse theory | Calculus of variations

Book

2011, Universitext, ISBN 1461411041, 366

.... This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory...

Morse theory

Morse theory

eBook

Journal of the European Mathematical Society, ISSN 1435-9855, 2013, Volume 15, Issue 3, pp. 969 - 995

.... Our techniques include convex surface theory, Legendrian ruling invariants, and Heegaard–Floer homology.

General | Differential geometry | Manifolds and cell complexes | Legendrian knot | Twist knots | Transverse knot | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Geometric Topology | Symplectic Geometry

General | Differential geometry | Manifolds and cell complexes | Legendrian knot | Twist knots | Transverse knot | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Geometric Topology | Symplectic Geometry

Journal Article

2011, 1. Aufl., Modern Birkhauser Classics, ISBN 3034801033, 352

...: symplectic topology. Surprising rigidity phenomena demonstrate that the nature of symplectic mappings is very different from that of volume preserving mappings...

Mathematics | Congresses

Mathematics | Congresses

eBook

2014, Bolyai Society Mathematical Studies, ISBN 3319020358, Volume 26

In a pair of seminal papers Peter Ozsváth and Zoltan Szabó defined a collection of homology groups associated to a 3-manifold they named Heegaard-Floer homologies...

Contact Structure | Dehn Twist | Convex Boundary | Contact Manifold | Maslov Index

Contact Structure | Dehn Twist | Convex Boundary | Contact Manifold | Maslov Index

Book Chapter

Quantum topology, ISSN 1663-487X, 2018, Volume 9, Issue 1, pp. 167 - 205

We introduce a class of links strictly containing quasi-alternating links for which mod 2 reduced Khovanov homology is always thin...

Khovanov homology | Quasi-alternating | Instanton homology | Knots | Quantum Science & Technology | Physical Sciences | Mathematics | Physics | Science & Technology

Khovanov homology | Quasi-alternating | Instanton homology | Knots | Quantum Science & Technology | Physical Sciences | Mathematics | Physics | Science & Technology

Journal Article

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