Explore the applications of winding numbers in algebraic topology in this 27-minute lecture from the Insights into Mathematics series. Define the degree of a function from the circle to the circle and use this concept to demonstrate that there is no retraction from the disk to the circle. Delve into the Brouwer fixed point theorem and examine a Lemma of Borsuk. Learn about continuous maps, their definitions, and the concept of antipodes as part of this beginner's course in algebraic topology, presented by Associate Professor N J Wildberger at UNSW.
More Applications of Winding Numbers - Algebraic Topology - NJ Wildberger
Insights into Mathematics via YouTube
Overview
Syllabus
Introduction
Continuous maps
Defining continuous maps
Brauer fixed point theorem
Antipodes
Taught by
Insights into Mathematics
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