MIT Topology Seminar
Monday, November 8, 2004
Room 2-131, 4:30pm
Tom Goodwillie will speak on:
Tate spectra and Taylor towers
Abstract: I will discuss two closely related theorems of Nick Kuhn about telescopic localization L=L_{T(n)}. Part of the fun is that at first glance the theorems do not look very closely related; one is about group actions on spectra, while the other is about calculus of functors. The first theorem says that when a finite group acts on a local spectrum then the Tate spectrum is acyclic. The second says that for a functor from spectra to spectra the localization of the Taylor tower always splits. The second theorem is deduced from the first, and the first is proved using a special case of the second. Ultimately they both rely on Kuhn's result that L factors through the functor $\Omega^{\infty}$.