Algebraic & Geometric Topology

$I$–adic towers in topology

Samuel Wüthrich

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Abstract

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.

Article information

Source
Algebr. Geom. Topol., Volume 5, Number 4 (2005), 1589-1635.

Dates
Received: 15 June 2005
Revised: 9 November 2005
Accepted: 15 November 2005
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796492

Digital Object Identifier
doi:10.2140/agt.2005.5.1589

Mathematical Reviews number (MathSciNet)
MR2186112

Zentralblatt MATH identifier
1107.55007

Subjects
Primary: 55P42: Stable homotopy theory, spectra 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) 55T15: Adams spectral sequences
Secondary: 55U20: Universal coefficient theorems, Bockstein operator 55P60: Localization and completion 55N22: Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]

Keywords
structured ring spectra Adams resolution Adams spectral sequence Bockstein operation complex cobordism Morava $K$–theory Bousfield localization stable homotopy theory.

Citation

Wüthrich, Samuel. $I$–adic towers in topology. Algebr. Geom. Topol. 5 (2005), no. 4, 1589--1635. doi:10.2140/agt.2005.5.1589. https://projecteuclid.org/euclid.agt/1513796492


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