Abstract for ``The Bousfield-Kan spectral sequence for periodic
homology theories'' by Martin Bendersky and Rob Thompson.
AMS classification numbers: Primary 55Q40; Secondary 55P60, 55T15,
55H20, 19L99.
Author addresses: Hunter College, CUNY
Department of Mathematics and Statistics
695 Park Ave.
New York, NY 10021



In this paper we construct the Bousfield-Kan (unstable Adams) spectral sequence based on certain non-connective periodic homology theories E such as complex periodic K-theory, and define an E-completion of a space X. For X = S^{2n+1} and E = K we calculate the E_2-term and show that the spectral sequence converges to the homotopy groups of the K-completion of the sphere. This also determines all of the homotopy groups of the (unstable) K-theory localization of S^{2n+1} including three divisible groups in negative stems.