Relative Homotopy Groups

This lecture introduces relative homotopy groups, focusing on establishing a long exact sequence for any pair of spaces. The instructor discusses the application of this theory, the structure of homotopic classes, and the group structure on pairs using the Ekman-Hilton trick. The lecture also covers the relationship between absolute and relative homotopy groups, the boundary operator, and the compression lemma to identify the neutral element. Additionally, the instructor explains how to construct maps representing the unit in homotopy groups and defines the boundary homomorphism. The lecture concludes with the derivation of the long exact sequence for homotopy groups of pairs.