Legendrian torus knots in S1 × S2
نویسندگان
چکیده
منابع مشابه
Classical invariants of Legendrian knots in the 3-dimensional torus
All knots in R3 possess Seifert surfaces, and so the classical Thurston-Bennequin invariant for Legendrian knots in a contact structure on R 3 can be defined. The definitions extend easily to null-homologous knots in a 3-manifold M endowed with a contact structure ξ. We generalize the definition of Seifert surfaces and use them to define the Thurston-Bennequin invariant for all Legendrian knots...
متن کاملStudying Uniform Thickness I: Legendrian Simple Iterated Torus Knots
We prove that the class of topological knot types that are both Legendrian simple and satisfy the uniform thickness property (UTP) is closed under cabling. An immediate application is that all iterated cabling knot types that begin with negative torus knots are Legendrian simple. We also examine, for arbitrary numbers of iterations, iterated cablings that begin with positive torus knots, and es...
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 کاملTopologically Trivial Legendrian Knots
This paper deals with topologically trivial Legendrian knots in tight and overtwisted contact 3-manifolds. The first parts (Sections 1-3) contain a thorough exposition of the proof of the classification of topologically trivial Legendrian knots (i.e. Legendrian knots bounding embedded 2-disks) in tight contact 3-manifolds (Theorem 1.7), and, in particular, in the standard contact S. These parts...
متن کاملLegendrian Solid-torus Links
Differential graded algebra invariants are constructed for Legendrian links in the 1-jet space of the circle. In parallel to the theory for R, Poincaré–Chekanov polynomials and characteristic algebras can be associated to such links. The theory is applied to distinguish various knots, as well as links that are closures of Legendrian versions of rational tangles. For a large number of two-compon...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2015
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216515500649