Mapping Cones and Fiber Sequences

This lecture covers the construction of mapping cones and fiber sequences, demonstrating how to extend maps from suspensions to cones and cylinders. The instructor explains the process of collapsing cones and mapping spaces, illustrating the concept of homotopy equivalence and exact sequences. The lecture delves into the duality between mapping cones and mapping fibers, showcasing the relationship between loops and evaluation maps. Through a series of examples and diagrams, the instructor elucidates the theory behind mapping spaces and their role in homotopy theory.