منابع مشابه
New Invariants of Legendrian Knots
We discuss two different ways to construct new invariants of Legendrian knots in the standard contact R. These invariants are defined combinatorially, in terms of certain planar projections, and (sometimes) allow to distinguish Legendrian knots which are not Legendrian isotopic but have the same classical invariants.
متن کاملInvariants of Legendrian Knots and Coherent Orientations
We provide a translation between Chekanov’s combinatorial theory for invariants of Legendrian knots in the standard contact R and a relative version of Eliashberg and Hofer’s contact homology. We use this translation to transport the idea of “coherent orientations” from the contact homology world to Chekanov’s combinatorial setting. As a result, we obtain a lifting of Chekanov’s differential gr...
متن کاملOn Legendrian Knots and Polynomial Invariants
It is proved in this note that the analogues of the Bennequin inequality which provide an upper bound for the Bennequin invariant of a Legendrian knot in the standard contact three dimensional space in terms of the lower degree in the framing variable of the HOMFLY and the Kauffman polynomials are not sharp. Furthermore, the relationships between these restrictions on the range of the Bennequin...
متن کاملInvariants of Legendrian Knots from Open Book Decompositions
In this note, we define a new invariant of a Legendrian knot in a contact manifold using an open book decomposition supporting the contact structure. We define the support genus sg(L) of a Legendrian knot L in a contact 3-manifold (M, ξ) as the minimal genus of a page of an open book of M supporting the contact structure ξ such that L sits on a page and the framing given by the contact structur...
متن کاملClassical 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...
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ژورنال
عنوان ژورنال: Quantum Topology
سال: 2015
ISSN: 1663-487X
DOI: 10.4171/qt/66