LEGENDRIAN KNOTS AND LINKS CLASSIFIED BY CLASSICAL INVARIANTS
نویسندگان
چکیده
منابع مشابه
Legendrian Knots and Links Classified by Classical Invariants
It is shown that Legendrian (resp. transverse) cable links in S with its standard tight contact structure, i.e. links consisting of an unknot and a cable of that unknot, are classified by their oriented link type and the classical invariants (Thurston-Bennequin invariant and rotation number in the Legendrian case, self-linking number in the transverse case). The analogous result is proved for t...
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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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.
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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 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...
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ژورنال
عنوان ژورنال: Communications in Contemporary Mathematics
سال: 2007
ISSN: 0219-1997,1793-6683
DOI: 10.1142/s0219199707002381