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

This 25-page paper by Martin Bendersky and Donald M. Davis appeared in the Proceedings of the 1999 conference at Stanford University of Algebraic Topology and its Interactions. It was published in American Math Society Contemporary Math 279 (2001) 37-56.

dvi file and ps file.

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