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Higher genus knot contact homology and recursion for colored HOMFLY-PT polynomials

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Date
2020-01-01
Authors
Ekholm, T
Ng, L
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Abstract
We sketch a construction of Legendrian Symplectic Field Theory (SFT) for conormal tori of knots and links. Using large N duality and Witten’s connection between open Gromov–Witten invariants and Chern–Simons gauge theory, we relate the SFT of a link conormal to the colored HOMFLY-PT polynomials of the link. We present an argument that the HOMFLY-PT wave function is determined from SFT by induction on Euler characteristic, and also show how to, more directly, extract its recursion relation by elimination theory applied to finitely many noncommutative equations. The latter can be viewed as the higher genus counterpart of the relation between the augmentation variety and Gromov–Witten disk potentials established in [1] by Aganagic, Vafa, and the authors, and, from this perspective, our results can be seen as an SFT approach to quantizing the augmentation variety
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Journal article
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https://hdl.handle.net/10161/26367
Published Version (Please cite this version)
10.4310/ATMP.2020.V24.N8.A3
Publication Info
Ekholm, T; & Ng, L (2020). Higher genus knot contact homology and recursion for colored HOMFLY-PT polynomials. Advances in Theoretical and Mathematical Physics, 24(8). pp. 2067-2145. 10.4310/ATMP.2020.V24.N8.A3. Retrieved from https://hdl.handle.net/10161/26367.
This is constructed from limited available data and may be imprecise. To cite this article, please review & use the official citation provided by the journal.
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Scholars@Duke

Ng

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
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