Homotopy

In this video we introduce the notion of homotopy, an indispensable tool in topology. Continuous maps are homotopic essentially when they are continuous deformations of each other. Many algebraic invariants used in algebraic topology cannot distinguish between homotopic maps, which is why we need to study them. We will look at the basic definition of homotopies, and see how they give a new homotopy category which may be viewed as a coarse way to study topological spaces, where homotopic maps are identified. Homotopy theory concerns studying topological spaces up to isomorphisms in this category, the homotopy equivalences. We will look at this notion in the simple case of contractible spaces, those homotopy equivalent to a point.

[김현학-ph]

Thank you for the interesting lectures. You explained so well that it's easy to understand.