منابع مشابه
Lagrangian 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...
متن کاملLegendrian 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...
متن کاملLegendrian Surgeries on Stabilized Legendrian Links
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 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 کاملBraid-positive Legendrian links
Any link that is the closure of a positive braid has a natural Legendrian representative. These were introduced in [15], where their Chekanov– Eliashberg contact homology was also evaluated. In this paper we rephrase and improve that computation using a matrix representation. In particular, we present a way of finding all augmentations of such Legendrians, construct an augmentation which is als...
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ژورنال
عنوان ژورنال: Asian Journal of Mathematics
سال: 2001
ISSN: 1093-6106,1945-0036
DOI: 10.4310/ajm.2001.v5.n1.a8