Universal Coefficient Theorems

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Introduces reduced homology groups and explains their properties and applications in topology.

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

Explains relative homology, n-cycles, n-boundaries, and exact sequences of chain complexes.

Focuses on lifting properties in homotopy theory of chain complexes.

Covers the structure of topological spaces with A-complexes and chain complexes.

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

Introduces cohomology, focusing on abelian cochains and their correspondence with singular cochains.

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

Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.

Covers induced homomorphisms, homotopy invariance, and homology groups of quotients.

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

Explores the Mayer-Vietoris sequence, exact homomorphisms, embedded spheres, and path-connected spaces.

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