Homology and the fundamental group

Related lectures (33)

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

Covers the concept of excision in algebraic topology with a focus on simplicial and singular homology.

Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.

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

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

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

Introduces the concept of homology groups and focuses on a lemma about free abelian groups.

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

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

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

Covers induced homomorphisms on relative homology groups and their properties.

Delves into applying cellular homology to compute homology groups and Euler characteristic, showcasing its practical implications.

Covers extensions to exchangeability in network data analysis, including graphon frameworks and edge exchangeability.

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