## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**Title:** The Chromatic Splitting Conjecture at $n=p=2$

**Speaker:** Agnes Beaudry

**Speaker Info:** University of Chicago

**Brief Description:**

**Special Note**: **Note unusual day, time and room!**

**Abstract:**

In its strongest form, the chromatic splitting conjecture gives a
precise description of the homotopy type of $L_{1}L_{K(2)}S$, which has been shown to hold for $p\geq 5$ by Hopkins and for $p=3$ by Goerss, Henn and Mahowald. In this talk, I will explain why this description cannot hold at the prime $p=2$. More precisely, let $V(0)$ be the mod $2$ Moore spectrum. I will give a summary of how one uses the duality resolution techniques to show that $\pi_{k}L_1L_{K(2)}V(0)$ is not zero when $k$ is congruent to $5$ modulo $8$. I will explain how this contradicts the decomposition of $L_1L_{K(2)}S$ predicted by the chromatic splitting conjecture.

**Date:** Thursday, April 30, 2015

**Time:** 3pm

**Where:** Lunt 107

**Contact Person:** Prof. Paul Goerss

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

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

Copyright © 1997-2024
Department of Mathematics, Northwestern University.