ON ARC INDEX AND MAXIMAL THURSTON–BENNEQUIN NUMBER

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2012-04

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Abstract

We discuss the relation between arc index, maximal ThurstonBennequin number, and Khovanov homology for knots. As a consequence, we calculate the arc index and maximal ThurstonBennequin number for all knots with at most 11 crossings. For some of these knots, the calculation requires a consideration of cables which also allows us to compute the maximal self-linking number for all knots with at most 11 crossings. © 2012 World Scientific Publishing Company.

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10.1142/S0218216511009820

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Ng, L (2012). ON ARC INDEX AND MAXIMAL THURSTON–BENNEQUIN NUMBER. Journal of Knot Theory and Its Ramifications, 21(04). pp. 1250031–1250031. 10.1142/S0218216511009820 Retrieved from https://hdl.handle.net/10161/17789.

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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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