Chapter 5: The Adams Spectral Sequence

Abstract

As we demonstrated in the previous lecture, the information about the action of stable cohomology operations may be used for computing stable homotopy groups. If we know the cohomology of the space X, we can find, relatively easily, the “stable part” of the cohomology of the first killing space of X, and then the same for the second, the third, and so on killing spaces. Hurewicz’s theorem gives us, every time, the corresponding homotopy group. This method (the Serre method) does not permit us, however, to find the homotopy groups without dealing with other difficulties.