AlgTop5: Two-dimensional objects- the torus and genus

We introduce some surfaces: the cylinder, the torus or doughnut, and the n-holed torus. We define the genus of a surface in terms of maximal number of disjoint curves that do not disconnect it. We discuss how the plane covers the cylinder and the torus, and the associated group of translations.

This is the 5th lecture of this beginners course in Algebraic Topology given by Assoc Prof N J Wildberger of UNSW.

His YouTube site Insights into Mathematics at user: njwildberger also contains series on MathFoundations, History of Mathematics, LinearAlgebra, Rational Trigonometry and even one called Elementary Mathematics (K-6) Explained.