Topology of Riemann Surfaces

This lecture covers the topology of Riemann surfaces, focusing on the triangulation of compact Riemann surfaces using finitely many triangles. The instructor explains the concept of a triangulation, where a compact Riemann surface can be represented as a polygon with edges. The lecture emphasizes the requirement for two triangles to be either disjoint, intersect at a single vertex, or intersect along an edge. Furthermore, it discusses the theorem that any compact Riemann surface can be triangulized, providing a detailed proof. The lecture also delves into the planar model of a surface, illustrating how a planar diagram can be used to represent the surface.