Long Exact Sequence in Homotopy

This lecture covers the concept of a long exact sequence in homotopy, starting with the subspace inclusion notation and the induced maps between homotopy classes. The lecture explains the boundary homomorphisms and the exact sequence involving relative homotopy groups, emphasizing the importance of sets and groups in the sequence. The instructor demonstrates the application of the Cellular Approximation Theorem and the CW Approximation Theorem in the context of CW complexes and polyhedra, highlighting the significance of cellular maps and their implications on homotopy groups. The lecture concludes with a discussion on constructing homotopies on polyhedra to establish a long exact sequence in a general setting.