Homology: Introduction and Applications

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Related lectures (31)

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Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Serre model structure on Top

Explores the Serre model structure on Top, focusing on right and left homotopy.

CW Approximation Theorem

Explores the CW Approximation Theorem, constructing CW complexes from spaces to ensure isomorphism on homology groups.

Shape of Data: Algebraic Topology and Shape Representation

Covers algebraic topology, Betti numbers, and shape representation methods for efficient data shape measurement and analysis.

Homotopy Invariance: Homology Groups

Explores homotopy invariance and its application to homology groups of quotients, showcasing isomorphism and chain homotopy.

Topology: Homotopy and Cone Attachments

Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.

Cellular Homology

Explains cellular homology and the computation of homology groups using boundary maps.

Topology: Fundamental Groups and Applications

Provides an overview of fundamental groups in topology and their applications, focusing on the Seifert-van Kampen theorem and its implications for computing fundamental groups.

Homology groups: Quotients

Covers homology groups of quotients, homotopy invariance, and exact sequences.

Homology with coefficients

Covers homology with coefficients, introducing the concept of defining homology groups with respect to arbitrary abelian groups.