The topology of singular points of real analytic curves

In the neighborhood of a singular point, a real analytic curve in the plane consists of a finite number of branches. Each of these branches intersects a small circle around the singular point in two points. Therefore, the local topology is described by a chord diagram: an even number of points on a circle paired two by two. Not all chord diagrams come from a singular point. The main purpose of this talk is to give an complete description of those «analytic» chord diagrams. On our way, we shall meet some interesting concepts from computer science, graph theory.