## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**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.

**Date:** Monday, November 6, 2000

**Time:** 4:10pm

**Where:** Lunt 104

**Contact Person:** Prof. Paul Goerss

**Contact email:** pgoerss@math.nwu.edu

**Contact Phone:** 847-491-8544

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