Classification of 2-Manifolds and Euler Characteristic - Differential Geometry

Explore the classification of compact, oriented 2-manifolds and their relation to the Euler characteristic in this differential geometry lecture. Learn about the combinatorial approach of decomposing 2-manifolds into polygon pieces, performing cut and paste operations to achieve normal forms. Discover the foundational work of Dehn and Heegaard from 1910, which led to a complete classification of orientable surfaces based solely on the Euler invariant. Gain insights into this crucial result in differential geometry and algebraic topology, understanding its significance for both fields.

Introduction
Classification strategy
Example
Reducing the number of vertices
Reducing the number of edges
Topology
Euler characteristic
Summary