Math @ Duke

Publications [#243939] of Lenhard L. Ng
Papers Published
 Ng, L; Rutherford, D, Satellites of Legendrian knots and representations of the ChekanovEliashberg Algebra,
Algebraic and Geometric Topology, vol. 13 no. 5
(2013),
pp. 30473097, ISSN 14722747 [arXiv:1206.2259], [doi]
(last updated on 2018/02/21)
Abstract: We develop a close relation between satellites of Legendrian knots in ℝ3 and the ChekanovEliashberg differential graded algebra of the knot. In particular, we generalize the wellknown correspondence between rulings of a Legendrian knot in ℝ3 and augmentations of its DGA by showing that the DGA has finitedimensional representations if and only if there exist certain rulings of satellites of the knot. We derive several consequences of this result, notably that the question of existence of ungraded finitedimensional representations for the DGA of a Legendrian knot depends only on the topological type and ThurstonBennequin number of the knot.


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