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The Bousfield-Kan spectral sequence for periodic homology theories
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 122, Number 3, June 2000
- pp. 599-635
- 10.1353/ajm.2000.0015
- Article
- Additional Information
We construct the Bousfield-Kan (unstable Adams) spectral sequence based on certain nonconnective periodic homology theories E such as complex periodic K-theory, and define an E-completion of a space X. For X = S2n+1 and E = K we calculate the E2-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 S2n+1 including three divisible groups in negative stems.