Combinatorial knot contact homology and transverse knots

By Lenhard L. Ng. 2010

57 citations recorded by the source corpus.

Abstract We give a combinatorial treatment of transverse homology, a new invariant of transverse knots that is an extension of knot contact homology. The theory comes in several flavors, including one that is an invariant of topological knots and produces a three-variable knot polynomial related to the A -polynomial. We provide a number of computations of transverse homology that demonstrate its effectiveness in distinguishing transverse knots, including knots that cannot be distinguished by the Heegaard Floer transverse invariants or other previous invariants.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/344b619e6c090273e63e5227d424b3ae6b703404

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Citations in the corpus

Knot contact homology (2011, background): “There is a related combinatorial treatment in [26], where it is shown that this filtered version (“transverse homology”) constitutes a very effective invariant of transverse knots.”
Grid Homology for Knots and Links (2015, methodology): “Lenny Ng [156] has constructed another useful combinatorial invariant for transverse knots, inspired by methods from symplectic geometry.”
A topological introduction to knot contact homology (2012, methodology): “Then we have (1) φB(A) = Φ L B ·A ·Φ R B ; see [Ng08, Ng11] for the proof.”