Thu, December 3, 2015
3:00 pm - 4:00 pm
MA 105
Title: Computations in 2-local stable homotopy theory
Speaker: Philip Egger, Northwestern
Abstract: The subalgebra $A(1)$ of the mod 2 Steenrod algebra $A$ can be seen as an $A$-module in four different ways. Davis and Mahowald showed that all four of these $A$-modules are the mod 2 cohomologies of type 2 finite CW-complexes $A_1[ij]$ for $i,j\in\{0,1\}$. We prove that all four of these complexes admit a 32-periodic $v_2$-self-map. Time permitting, we discuss the search for a complex $Z$ which will admit a 1-periodic $v_2$-self-map, and possibly disprove the telescope conjecture at $n=p=2$.
This work is joint with Bhattacharya and Mahowald.