Local Degrees: Calculating Maps

This lecture explores the concept of local degrees of continuous maps from the sphere to itself, demonstrating their practical utility in calculating degrees of given maps. By examining commutative diagrams and isomorphisms, the instructor explains how local degrees are determined and how they can be used to calculate the overall degree of a map. Through examples, such as the degree of a homeomorphism and constructing maps of arbitrary degree, the lecture illustrates the application of local degrees in understanding and manipulating mappings on the sphere.