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Lecture

Local Degrees: Calculating Maps

In course

MATH-323: Topology III - Homology

Homology is one of the most important tools to study topological spaces and it plays an important role in many fields of mathematics. The aim of this course is to introduce this notion, understand its properties and learn how to compute it. There will be m ...

Description

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.

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Instructor

Leonid Monin

Official source

Ontological neighbourhood

Education

Educational stages: Higher education

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