Classification of 2-Manifolds and Euler Characteristic - Differential Geometry
Insights into Mathematics via YouTube
Overview
Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!
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.
Syllabus
Introduction
Classification strategy
Example
Reducing the number of vertices
Reducing the number of edges
Topology
Euler characteristic
Summary
Taught by
Insights into Mathematics