Obstructions to Lagrangian concordance
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2016-04-26
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Abstract
We investigate the question of the existence of a Lagrangian concordance between two Legendrian knots in $\mathbb{R}^3$. In particular, we give obstructions to a concordance from an arbitrary knot to the standard Legendrian unknot, in terms of normal rulings. We also place strong restrictions on knots that have concordances both to and from the unknot and construct an infinite family of knots with non-reversible concordances from the unknot. Finally, we use our obstructions to present a complete list of knots with up to 14 crossings that have Legendrian representatives that are Lagrangian slice.
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Cornwell, Christopher, Lenhard Ng and Steven Sivek (2016). Obstructions to Lagrangian concordance. Algebraic & Geometric Topology, 16(2). pp. 797–824. 10.2140/agt.2016.16.797 Retrieved from https://hdl.handle.net/10161/17779.
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Lenhard Lee Ng
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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