Links represented by phases of algebraic curves

Abstract

The prime motivation behind this paper is to prove that any torus link can be realized as the union of the one-dimensional connected components of the set of critical values of the argument map restricted to a complex algebraic plane curve. Moreover, we give an explicit relation between the Newton polygon of such plane curves, and the number of components of the given torus link. This work aims to represent the starting point for a connection between knot theory, tropical geometry, and (co)amoebas.