Lectures related to Homology and Homotopy

Introduces homology as a tool to distinguish spaces in all dimensions and provides insights into its construction and applications.

Explores the cellular approximation theorem for CW complexes and its implications on homotopy groups.

Covers the proof of Theorem A, discussing homology, quotients, and isomorphisms.

Explores the Serre model structure on Top, focusing on right and left homotopy.

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

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

Covers induced homomorphisms on relative homology groups and their properties.

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

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

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