Homology and the fundamental group

Related lectures (32)

Page 3 of 4

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.

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 Hopf formula in cohomology groups, emphasizing the 4-term exact sequence and its implications.

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 the cup product on cohomology, acyclic models, and the universal coefficient theorem.