Volume 5, issue 4 (2005)

 Recent Issues
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
$I$–adic towers in topology

Samuel Wüthrich

Algebraic & Geometric Topology 5 (2005) 1589–1635
 arXiv: math.AT/0411409
Abstract

A large variety of cohomology theories is derived from complex cobordism $M{U}^{\ast }\left(-\right)$ by localizing with respect to certain elements or by killing regular sequences in $M{U}_{\ast }$. 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 $Ê\left(n\right)$ and Morava $K$–theory $K\left(n\right)$ 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
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