Cabling and transverse simplicity
نویسندگان
چکیده
منابع مشابه
Cabling and Transverse Simplicity
We study Legendrian knots in a cabled knot type. Specifically, given a topological knot type K, we analyze the Legendrian knots in knot types obtained from K by cabling, in terms of Legendrian knots in the knot type K. As a corollary of this analysis, we show that the (2, 3)-cable of the (2, 3)-torus knot is not transversely simple and moreover classify the transverse knots in this knot type. T...
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HEEGAARD FLOER INVARIANTS AND CABLING Jennifer Hom Paul Melvin, Advisor A natural question in knot theory is to ask how certain properties of a knot behave under satellite operations. We will focus on the satellite operation of cabling, and on Heegaard Floertheoretic properties. In particular, we will give a formula for the Ozsváth-Szabó concordance invariant τ of iterated cables of a knot K in...
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We characterise the cabling operations on the weight systems of finite type knot invariants. The eigenvectors and eigenvalues of this family of operations are described. The canonical deframing projection for these knot invariants is described over the cable eigenbasis. The action of immanent weight systems on general Feynman diagrams is considered, and the highest eigenvalue cabling eigenvecto...
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The Burau representation enables to define many other representations of the braid group Bn by the topological operation of “cabling braids”. We show here that these representations split into copies of the Burau representation itself and of a representation of Bn/(Pn, Pn). In particular, we show that there is no gain in terms of faithfulness by cabling the Burau representation.
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2005
ISSN: 0003-486X
DOI: 10.4007/annals.2005.162.1305