The 1-line of the K-theory Bousfield-Kan spectral sequence for Spin(2n+1)

Abstract

For X a simply-connected finite H-space, there is a Bousfield-Kan spectral sequence which converges to the homotopy of its K-completion. When X=Spin(2n+1), we expect that these homotopy groups equal the v1-periodic homotopy groups in dimension greater than n^2. In this paper, we accomplish two things. (1) We prove that, for any X, the 1-line of this spectral sequence is determined in an explicit way from K-theory and Adams operations. (2) For X=Spin(2n+1), we make an explicit computation of this 1-line.