Volume 5, issue 4 (2005)

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$I$–adic towers in topology

Samuel Wüthrich

Algebraic & Geometric Topology 5 (2005) 1589–1635

arXiv: math.AT/0411409


A large variety of cohomology theories is derived from complex cobordism MU() by localizing with respect to certain elements or by killing regular sequences in MU. We study the relationship between certain pairs of such theories which differ by a regular sequence, by constructing topological analogues of algebraic I–adic towers. These give rise to Higher Bockstein spectral sequences, which turn out to be Adams spectral sequences in an appropriate sense. Particular attention is paid to the case of completed Johnson–Wilson theory Ê(n) and Morava K–theory K(n) for a given prime p.

structured ring spectra, Adams resolution, Adams spectral sequence, Bockstein operation, complex cobordism, Morava $K$–theory, Bousfield localization, stable homotopy theory.
Mathematical Subject Classification 2000
Primary: 55P42, 55P43, 55T15
Secondary: 55U20, 55P60, 55N22
Forward citations
Received: 15 June 2005
Revised: 9 November 2005
Accepted: 15 November 2005
Published: 24 November 2005
Samuel Wüthrich
Department of Pure Mathematics
University of Sheffield
Hicks Building
Hounsfield Road
Sheffield S3 7RH
United Kingdom