Lectures related to Homology Groups: Basics

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

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

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

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

Covers fundamental concepts of space, topology, groups, and homology theory.

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

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

Covers spaces, homology, chain groups, and abelianization in CW complexes and maps.

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

Explores the comparison of long exact sequences for vibrations and the relationship between homotopy and homology groups.