The correspondence between augmentations and rulings for Legendrian knots
نویسندگان
چکیده
منابع مشابه
The Correspondence between Augmentations and Rulings for Legendrian Knots
We strengthen the link between holomorphic and generatingfunction invariants of Legendrian knots by establishing a formula relating the number of augmentations of a knot’s contact homology to the complete ruling invariant of Chekanov and Pushkar.
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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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Contact structures on manifolds and Legendrian and transversal knots in them are very natural objects, born over two centuries ago, in the work of Huygens, Hamilton and Jacobi on geometric optics and work of Lie on partial differential equations. They touch on diverse areas of mathematics and physics, and have deep connections with topology and dynamics in low dimensions. The study of Legendria...
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We study satellites of Legendrian knots in R and their relation to the Chekanov–Eliashberg differential graded algebra of the knot. In particular, we generalize the well-known correspondence between rulings of a Legendrian knot in R and augmentations of its DGA by showing that the DGA has finite-dimensional representations if and only if there exist certain rulings of satellites of the knot. We...
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In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the m(52) knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least n different Legendrian representatives with maximal Thurston–Bennequin number of the twist knot K−2n with crossing number 2n+1. In this paper we give a complete classification of Legendrian and transverse representatives o...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2006
ISSN: 0030-8730
DOI: 10.2140/pjm.2006.224.141