EVENT DETAILS AND ABSTRACT

Title: Periodic homology of infinite loop spaces
Speaker: Professor Nick Kuhn
Speaker Info: University of Virginia
Brief Description:
Special Note:
Abstract:

The functor that assigns to a spectrum X the suspension spectrum of its 0th space admits a Goodwillie calculus resolution, with rth fiber equal to the rth extended power of X. If X is itself the suspension spectrum of a space, then this tower naturally splits: this is one form of the classic stable splitting theorem. Our new theorem is that, after localizing at any Morava K-theory K(n) (n > 0), the tower naturally splits for ALL spectra X. This has implications for computing the E-homology or cohomology of infinite loopspaces, where E is any theory Bousfield equivalent to some K(n), e.g. the theories E_n so important in the work of Hopkins and collaborators. The key ideas in the proof are related to previous work by Bousfield and me. In particular, the theorem follows easily from one of Pete's recent preprints. Like all work in this area, it is ultimately based on the nilpotence theorems of Devanitz, Hopkins, and Smith.