DiffGeom26: Classification of 2-manifolds and Euler characteristic

We describe the important classification of compact, oriented 2-manifolds, and the relation with the topological invariant called the Euler characteristic. The idea is to work combinatorially, by decomposing a 2-manifold into polygon pieces which are glued, or identified, along common edges, and then performing cut and paste operations to try to get such a configuration into a normal form. This was worked out by Dehn and Heegaard around 1910, and the resulting classification is one of the most important f