Krystyna Kuperberg - Shape Theory: Vietoris-Cech Approach to Homotopy

Explore shape theory, a Vietoris-type homotopy theory for compact metric spaces, in this 42-minute lecture by Krystyna Kuperberg. Delve into the origins of shape theory, introduced by K. Borsuk in the 1960s, and its advantages over more general theories like pro-category or étale homotopy. Discover how L. Vietoris extended the definition of the first homotopy group to arbitrary metric compacta in 1927, and learn about D. E. Christie's exploration of higher homotopy groups in 1944. Gain insights into the geometric approach of shape theory, which offers a simple yet sufficiently general method for understanding homotopy in compact metric spaces.