2-primary v 1-periodic homotopy groups of SU(n) revisited

Abstract

In 1991, Bendersky and Davis used the BP-based unstable Novikov spectral sequence to study the 2-primary v1-periodic homotopy groups of SU(n). Here we use a K-theoretic approach to add more detail to those results. In particular, whereas only the order of the groups was determined in the 1991 paper, here we determine the number of summands in these groups and much information about the orders of those summands. In addition, we give explicit conditions for certain differentials and extensions in a spectral sequence, which affect the homotopy groups. Finally, we give complete results for for n ≤ 13.