I–adic towers in topology

Wüthrich, Samuel

doi:10.2140/agt.2005.5.1589

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$I$–adic towers in topology

Samuel Wüthrich

Algebraic & Geometric Topology 5 (2005) 1589–1635

DOI: 10.2140/agt.2005.5.1589

arXiv: math.AT/0411409

Abstract

A large variety of cohomology theories is derived from complex cobordism $M U^{*} (-)$ by localizing with respect to certain elements or by killing regular sequences in $M U_{*}$ . 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 $p$ .

Keywords

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

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Publication

Received: 15 June 2005

Revised: 9 November 2005

Accepted: 15 November 2005

Published: 24 November 2005

Authors

Samuel Wüthrich
Department of Pure Mathematics University of Sheffield Hicks Building Hounsfield Road Sheffield S3 7RH United Kingdom

Volume 5, issue 4 (2005)