Analysis II Lecture 15 Part 3 Triangulations and the Euler characteristic
Channel: Arthur Parzygnat
Date: 19/05/2018

The idea behind a simplicial complex is given together with some examples. A triangulation of a manifold is a simplicial complex that approximates the manifold topologically. The Euler characteristic of a simplicial complex is defined and is invariant under simplicial homeomorphism. This can be used to define the Euler characteristic of a manifold via a triangulation. 

This is part of a series of lectures on Mathematical Analysis II. Topics covered include continuous and differentiable multi-variable functions on Euclidean space, the chain rule, the implicit function theorem, manifolds, tangent spaces, vector fields, the degree and index of a smooth map, the Euler characteristic, metric spaces, the contraction mapping theorem, existence and uniqueness of solutions to ordinary differential equations, and integral equations.

I speak rather slowly, so you may wish to increase the speed of this video.

These videos were created during the 2017 Spring semester at the UConn CETL Lightboard Room.