EVENT DETAILS AND ABSTRACT

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.