Two-Dimensional Objects - The Torus and Genus - Algebraic Topology

Explore the fundamental concepts of two-dimensional objects in algebraic topology through this 50-minute lecture. Delve into the properties of cylinders, tori, and n-holed tori, while learning to define the genus of a surface. Examine how the plane covers both cylinders and tori, and investigate the associated group of translations. Gain insights into Riemann's work in complex function theory and understand the significance of these concepts in modern mathematics.

Introduction
Cylinder
Open interval
Cylinder homomorphic
Group Theory
The torus
The genus
Configuration space
Orbit space
Tessellation