Singular homology

Related lectures (32)

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Covers the concept of simplicial homology, focusing on finite complexes and induced maps.

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Covers chain maps, homotopy invariance, homology groups, and induced homomorphisms between cycles and boundaries.

Covers the long exact sequence of relative homology groups and chain complexes.

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

Covers induced homomorphisms on relative homology groups and their properties.

Explores simplicial and singular homology, reduced homology groups, and their connection to the fundamental group.

Introduces singular homology, defining singular simplices and explaining the chain complex construction.

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

Covers the Zig Zag Lemma and the long exact sequence of relative homology.