Book ChapterDOI
Chapter 5 Contact geometry
Hansjörg Geiges
- Vol. 2, pp 315-382
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In this paper, the authors discuss some of the more fundamental differential topological aspects of contact geometry, such as classification questions in dimension 3, dynamics of the Reeb vector field, various notions of symplectic fillability, transverse, and Legendrian knots and links.Abstract:
Publisher Summary There are many excellent surveys covering specific aspects of contact geometry—for example, classification questions in dimension 3, dynamics of the Reeb vector field, various notions of symplectic fillability, transverse, and Legendrian knots and links. The chapter discusses some of the more fundamental differential topological aspects of contact geometry.read more
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D-instantons and twistors
TL;DR: In this article, the effects of all D-instantons in Type II string compactifications on Calabi-Yau three-folds were derived by recasting the previously known A-type D2-instanton corrections in the language of contact geometry, covariantizing the result under electromagnetic duality, and using mirror symmetry.
Journal ArticleDOI
Geometry of contact transformations and domains: orderability versus squeezing
TL;DR: Gromov's famous non-squeezing theorem (1985) states that the standard symplectic ball cannot be symplectically squeezed into any cylinder of smaller radius as discussed by the authors, and the answer depends on the sizes of the domains in question.
Journal ArticleDOI
Lagrangian concordance of Legendrian knots
TL;DR: In this paper, the authors define the notion of Lagrangian concordance between two Legendrian knots analogous to smooth concordances in the Legendrian context, and show that Legendrian isotopic Legendian knots are Lagrangians.
Journal ArticleDOI
The plastikstufe – a generalization of the overtwisted disk to higher dimensions
TL;DR: The first structural distinction found for contact 3-manifolds was the notion of overtwistedness as mentioned in this paper, which was based on the existence of a plastikstufe.
Journal ArticleDOI
Quantum mirror symmetry and twistors
TL;DR: Using the twistor approach to hypermultiplet moduli spaces, the authors derived the worldsheet, D(-1), and D1-instanton contributions to the generalized mirror map, relating Type IIA and Type IIB string theory compactified on generic mirror Calabi-Yau threefolds.
References
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Book
Mathematical Methods of Classical Mechanics
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
Mathematical methods of classical mechanics
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
Book
Knots and Links
TL;DR: In this paper, the fundamental group of three-dimensional PL geometry Seifert surfaces Finite cyclic coverings and the torsion invariants Infinite cyclic covers and the Alexander invariant Matrix invariants 3-manifolds and surgery on links Foliations, branched covers, fibrations and so on.
Journal ArticleDOI
Pseudo holomorphic curves in symplectic manifolds
TL;DR: In this article, the authors define a parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J).
Book
The Topology of Fibre Bundles.
TL;DR: In this paper, a succint introduction to fiber bundles is provided, which includes such topics as differentiable manifolds and covering spaces, and a brief survey of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles.