Knot theory and plane algebraic curves

Knot theory has been known for a long time to be a powerful tool for the study of the topology of local isolated singular points of a plane algebraic curve. However it is rather recently that knot theory has been used to study plane algebraic curves in the large. Given a reduced plane algebraic curve Γ − 2 passing through the origin, let Lr =Γ∩ ∂Br4 be the intersection of Γ with a round ball inC2 of radius r > 0 centered at the origin. When this intersection is transverse, Lr is an oriented link in Sr3 = ∂Br4. The main purpose of this paper is to present a survey of the results relating the topology of the pair (Sr3,Lr) to the topology of the pair (Br4,Γ∩ Br4).