Generalized normal rulings and invariants of Legendrian solid torus links
نویسندگان
چکیده
منابع مشابه
Legendrian 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 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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Each ruling of a Legendrian link can be naturally treated as a surface. For knots, the ruling is 2–graded if and only if the surface is orientable. For 2–graded rulings of homogeneous (in particular, alternating) knots, we prove that the genus of this surface is at most the genus of the knot. While this is not true in general, we do prove that the canonical genus (a.k.a. diagram genus) of any k...
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We show that the framed versions of the Kauuman and HOMFLY poly-nomials of a Legendrian link in the standard contact 3-space and solid torus are genuine polynomials in the framing variable. This proves a series of conjectures of 5] and provides estimates for the Bennequin{Tabachnikov numbers of such links. In a series of recent papers 1{3], V. I. Arnold revived interest in the study of plane cu...
متن کاملLegendrian 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...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2012
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.2012.258.393