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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

thompson@math.hunter.cuny.edu

http://math.hunter.cuny.edu/~benders

http://math.hunter.cuny.edu/~thompson

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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.

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