Algebraic Topology video lectures
Topology is a subject of fundamental importance in many branches of modern mathematics. Basically, it concerns properties of objects which remain unchanged under continuous deformation, which means by squeezing, stretching and twisting. Apples and oranges are topologically the same, but you can't deform an orange into a doughnut! More precisely, we can never deform in a continuous way a sphere (the surface of an orange) into a torus (the surface of a doughnut). Knots are also examples of topological objects, where a trefoil knot can never be deformed into an unknotted piece of string. The aim of this module is to explore properties of topological spaces. To distinguish topological spaces we will consider topological invariants such as the fundamental group, which is a powerful way of using algebra to detect topological features of spaces. The lecture notes for this course can be found by following the link below. They will be updated continually throughout the course. Exercises Mock Exams
The Hopf fibration shows how the three-sphere can be built by a collection of circles arranged like points on a two-sphere. This is a frame from an animation of fibers in the Hopf fibration over various points on the two-sphere. (Image and animation courtesy of Niles Johnson.
Lecture 1: AlgTop0 Introduction to Algebraic Topology
This is the Introductory lecture to a beginners course in Algebraic Topology given by N J Wildberger of the School of Mathematics and Statistics at UNSW in 2010. This first lecture introduces some of the topics of the course and three problems.
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