Numerical computations of complexification of Legendrian knots

Abstract

With the recent interest in knots, it is interesting to study their complexification. We have chosen to study Legendrian knots as they have the property that we can reconstruct the original knot from its projection. This property is especially useful in the case of the complexification of a knot as in this case the diagram of the projection of the knot is no longer real. In this paper we show a way to compute complex rational functions that have a Legendrian knot as an image under unit circle.