A topological introduction to knot contact homology

By Lenhard L. Ng. 2012

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Knot contact homology is a Floer-theoretic knot invariant derived from counting holomorphic curves in the cotangent bundle of \(\mathbb{R}^{3}\) with Lagrangian boundary condition on the conormal bundle to the knot. Among other things, this can be used to produce a three-variable polynomial that detects the unknot and conjecturally contains many known knot invariants; a different part of the package yields an effective invariant of transverse knots in \(\mathbb{R}^{3}\).

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/55b221c4efd95b0717b3954405fb5459746d1149