| I will review generalized cohomology theories and spectra as objects of the stable homotopy category. Ring structures in this category are important questions in homotopy theory. Generally, constructing ring structures on spectra is a difficult problem, but it is possible to do so in certain cases. The cohomology theories arising out of cobordism of manifolds give rise to Thom spectra. These were shown to have ring structures. Recently, a new way of constructing Thom spectra has been discovered by Ando, Blumberg, Gepner, Hopkins, and Rezk. We can apply classical methods for studying Thom spectra to study these new categories. |