Abstract: Generalized cohomology theories have been studied continuously since the late 1950's. My lecture of several weeks ago was devoted to a brief survey of topological K-theory, the first generalized cohomology theory to be developed and utilized. The present lecture will begin by discussing another family of generalized cohomology theories which have also been extensively studied - cobordism theory and its associated theories, notably Brown-Peterson theory and Morava K-theory. This work includes major contributions by Thom, Novikov and Quillen. A major theme of this discussion will be the algebra of cohomology operations associated with each of these theories.

As we will see, topological K-theory can also be fitted into the framework of this family of cohomology theories. In addition we will return to K-theory and discuss both operations and Adams operations. However these operations will turn out out be rather distinct from the ones considered for cobordism and BP theory.