Maximal Bennequin numbers and Kauffman polynomials of positive links
نویسندگان
چکیده
منابع مشابه
Maximal Thurston–bennequin Number of +adequate Links
The class of +adequate links contains both alternating and positive links. Generalizing results of Tanaka (for the positive case) and Ng (for the alternating case), we construct fronts of an arbitrary +adequate link A so that the diagram has a ruling; therefore its Thurston–Bennequin number is maximal among Legendrian representatives of A. We derive consequences for the Kauffman polynomial and ...
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Following the recent work by Chan [4] and Morton and Hadji [7] on the Homflypt polynomials of some generalized Hopf links, we investigate the Kauffman polynomials of generalized Hopf links. By studying the Kauffman skein module of the solid torus S × D, we establish a similar skein map on the Kauffman skein module of S × D which has distinct eigenvalues. Furthermore we are able to calculate the...
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We compute the maximal Thurston-Bennequin number for a Legendrian two-bridge knot or oriented two-bridge link in standard contact R, by showing that the upper bound given by the Kauffman polynomial is sharp. As an application, we present a table of maximal Thurston-Bennequin numbers for prime knots with nine or fewer crossings.
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We calculate the dimensions of the space of Vassiliev invariants coming from the Homfly polynomial of links, and of the space of Vassiliev invariants coming from the Kauffman polynomial of links. We show that the intersection of these spaces is spanned by the Vassiliev invariants coming from the Jones polynomial and from a polynomial called Υ. We also show that linearly independent Vassiliev in...
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A contact structure in a 3-dimensional manifold is a completely nonintegrable 2-dimensional distribution: if the distribution is the kernel of a (locally defined) 1-form λ then λ∧dλ = 0 everywhere. The standard contact structure in 3-space, arising from the identification of R with the space of 1-jets of functions on the line, is given by the contact form λ = dz−y dx; here x is a point on the l...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04983-7