EVENT DETAILS AND ABSTRACT

Title: On 2-local finite complexes and v_2-self-maps
Speaker: Philip Egger
Speaker Info: Northwestern
Brief Description: Thesis defense
Special Note:
Abstract:

A common method for finding large-scale periodic phenomena in the p-local homotopy groups of spheres involves finding finite CW complexes with self-maps that are non-nilpotent. Devinatz, Hopkins and Smith gave a systematic way of finding complexes admitting self-maps that are isomorphisms under Morava K-theory K(n)_*, known as v_n-self-maps. However, finding the periodicity of the resulting phenomena in the homotopy groups of spheres is hard. In joint work with Bhattacharya and Mahowald, we consider the case n=p=2 and establish the periodicity of the v_2-self-maps on 8-cell complexes A_1[ij] for i,j\in\{0,1\}. We then construct a 32-cell complex Z whose v_2-self-map we hope will have lower periodicity.