The 𝛼-family in the 𝐾(2)-local sphere at the prime 2

Abstract

In this note, we compute the image of the α-family in the homotopy of the K(2)-local sphere at the prime p = 2 by locating its image in the algebraic duality spectral sequence. This is a stepping stone for the computation of the homotopy groups of the K(2)-local sphere at the prime 2 using the duality spectral sequences.