Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

It is a classical theorem in algebraic topology that the n-th cohomology group of a space is isomorphic to the group of homotopy classes of maps from the space to K(G,n), where G is the coefficient group, and K(G,n) is the Eilenberg-MacLane space. Furthermore, it is known that the loop space of K(G,n) is homotopy equivalent to K(G,n-1). Thus we get a sequence of K(G,n), where n=1,2,3....., and leads to the theory of spectra. We will define what a spectrum is, explain how it defines a cohomology theory, and see some applications.