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We discuss higher dimensional homotopy groups, highlighting the difficulty of calculating them for even spheres, motivating the shift to homology which is easier to calculate. Then we define simplicial complexes, and the more general delta-complexes, and show how we use these to create a chain complex with a boundary operating relating the abelian groups with basis the n-simplicies. We give several examples of calculating simplicial homology, including the disk, circle, sphere, and torus.
Presented by Anthony Bosman, PhD.
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In this course we are following Hatcher, Algebraic Topology: [ Ссылка ]
