Satellites of Legendrian knots and representations of the Chekanov–Eliashberg algebra

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2013-08-01

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Abstract

We develop a close relation between satellites of Legendrian knots in ℝ3and the Chekanov-Eliashberg differential graded algebra of the knot. In particular, we generalize the well-known correspondence between rulings of a Legendrian knot in ℝ3and 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 derive several consequences of this result, notably that the question of existence of ungraded finite-dimensional representations for the DGA of a Legendrian knot depends only on the topological type and Thurston-Bennequin number of the knot.

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10.2140/agt.2013.13.3047

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Ng, L, and D Rutherford (2013). Satellites of Legendrian knots and representations of the Chekanov–Eliashberg algebra. Algebraic & Geometric Topology, 13(5). pp. 3047–3097. 10.2140/agt.2013.13.3047 Retrieved from https://hdl.handle.net/10161/17787.

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Lenhard Lee Ng

Professor of Mathematics

My research mainly focuses on symplectic topology and low-dimensional topology. I am interested in studying structures in symplectic and contact geometry (Weinstein manifolds, contact manifolds, Legendrian and transverse knots), especially through holomorphic-curve techniques. One particular interest is extracting topological information about knots through cotangent bundles, and exploring relations to topological string theory. I have also worked in Heegaard Floer theory, quantum topology, and sheaf theory, especially as they relate to Legendrian and transverse knots.


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