Topology Learning Seminar

William Gollinger

The Adams Spectral Sequence: Construction of the Adams Spectral Sequence

Now that we are equipped with the context of the stable homotopy category we can perform our construction. We will introduce resolutions of spectra and show how a resolution produces a spectral sequence. Identifying the terms of the resulting spectral sequence is unapproachable without additional assumptions, and we define an Adams Resolution to satisfy some homotopically exhaustive conditions. Using these conditions we can identify our E_2 page in terms of the Ext functor, and the E_\infty page in terms of the (p-completed) homotopy groups.

MC 5417