Chain Homotopy and Projective Complexes

Related lectures (31)

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

Explores the homotopy theory of chain complexes, including path object construction and fibrations.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores constructing a base B for a topology using homotopy classes and paths.

Introduces the concept of a universal covering construction with examples like Hawaiian rings.

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

Explores the homotopy theory of chain complexes over a field, focusing on closure properties and decomposition.

Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.

Discusses the classification of surfaces and their fundamental groups using the Seifert-van Kampen theorem and polygonal presentations.

Covers induced homomorphisms on relative homology groups and their properties.