منابع مشابه
Legendrian Mirrors and Legendrian Isotopy
We resolve a question of Fuchs and Tabachnikov by showing that there is a Legendrian knot in standard contact R with zero Maslov number which is not Legendrian isotopic to its mirror. The proof uses the differential graded algebras of Chekanov. A Legendrian knot in standard contact R is a knot which is everywhere tangent to the two-plane distribution induced by the contact one-form dz− y dx. Tw...
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We use Seiberg-Witten monopoles and Ozsváth-Szabó invariants to distinguish between tight contact structures obtained by Legendrian surgeries on stabilized Legendrian links in tight contact 3-manifolds.
متن کاملLegendrian and Transversal Knots
Contact structures on manifolds and Legendrian and transversal knots in them are very natural objects, born over two centuries ago, in the work of Huygens, Hamilton and Jacobi on geometric optics and work of Lie on partial differential equations. They touch on diverse areas of mathematics and physics, and have deep connections with topology and dynamics in low dimensions. The study of Legendria...
متن کاملIsotopies of Legendrian 1-knots and Legendrian 2-tori
We construct a Legendrian 2-torus in the 1-jet space of S × R (or of R) from a loop of Legendrian knots in the 1-jet space of R. The differential graded algebra (DGA) for the Legendrian contact homology of the torus is explicitly computed in terms of the DGA of the knot and the monodromy operator of the loop. The contact homology of the torus is shown to depend only on the chain homotopy type o...
متن کاملLagrangian and Legendrian Singularities
These are notes of the mini-courses we lectured in Trieste in 2003 and Luminy in 2004. The courses were based on the books [1, 3, 2]. A symplectic form ω on a manifold M is a closed 2-form, non-degenerate as a skew-symmetric bilinear form on the tangent space at each point. So dω = 0 and ω n is a volume form, dim M = 2n. Manifold M equipped with a symplectic form is called symplectic. It is nec...
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ژورنال
عنوان ژورنال: The Journal of Geometric Analysis
سال: 2014
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-014-9506-1