Geometry and Topology Seminar

An algebraic knot is the link of an isolated singular point on a unibranched plane complex curve. We will introduce the Puiseux characteristic sequence and the semigroup of algebraic knots. Then we will introduce the Upsilon function recently defined by Ozsvath, Stipsicz and Szabo. The Upsilon function of an algebraic knot can be represented by its semigroup. We will prove that the location of the first singularity of this function is determined by the least generator of the semigroup. As an application, we will give genus bounds for cobordisms between algebraic knots.