Computing Homology Groups - Algebraic Topology - NJ Wildberger
Offered By: Insights into Mathematics via YouTube
Course Description
Overview
Explore the concept of homology groups in algebraic topology through an in-depth examination of simple examples like the circle and disk. Learn how to define homology groups H_n(X) for a space X, understand the abstract process of considering complexes of abelian groups, and grasp the significance of boundary maps. Discover how different dimensions of homology groups measure various aspects of a space, such as connectivity, non-trivial loops, and 2-dimensional holes. Gain insights into the mathematical foundations of topology and develop a deeper understanding of how these abstract concepts relate to geometric structures.
Syllabus
Introduction
Circle
Boundary
quotient
connected space
disk
Taught by
Insights into Mathematics
Related Courses
Introduction to Algebraic Topology (Part-I)Indian Institute of Technology Bombay via Swayam Introduction to Algebraic Topology (Part-II)
NPTEL via Swayam Intro to the Fundamental Group - Algebraic Topology with Tom Rocks Maths
Dr Trefor Bazett via YouTube Neural Sense Relations and Consciousness - A Diagrammatic Approach
Models of Consciousness Conferences via YouTube Classification of 2-Manifolds and Euler Characteristic - Differential Geometry
Insights into Mathematics via YouTube