The cardinality of the augmentation category of a Legendrian link

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2017

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Abstract

We introduce a notion of cardinality for the augmentation category associated to a Legendrian knot or link in standard contact R3. This ℓhomotopy cardinality' is an invariant of the category and allows for a weighted count of augmentations, which we prove to be determined by the ruling polynomial of the link. We present an application to the augmentation category of doubly Lagrangian slice knots.

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10.4310/MRL.2017.v24.n6.a14

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Ng, L, D Rutherford, V Shende and S Sivek (2017). The cardinality of the augmentation category of a Legendrian link. Mathematical Research Letters, 24(6). pp. 1845–1874. 10.4310/MRL.2017.v24.n6.a14 Retrieved from https://hdl.handle.net/10161/17780.

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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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