Algebraic & Geometric Topology

Cellular approximations and the Eilenberg–Moore spectral sequence

Shoham Shamir

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Abstract

We set up machinery for recognizing k–cellular modules and k–cellular approximations, where k is an R–module and R is either a ring or a ring-spectrum. Using this machinery we can identify the target of the Eilenberg–Moore cohomology spectral sequence for a fibration in various cases. In this manner we get new proofs for known results concerning the Eilenberg–Moore spectral sequence and generalize another result.

Article information

Source
Algebr. Geom. Topol., Volume 9, Number 3 (2009), 1309-1340.

Dates
Received: 13 December 2007
Revised: 17 April 2009
Accepted: 19 April 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513797031

Digital Object Identifier
doi:10.2140/agt.2009.9.1309

Mathematical Reviews number (MathSciNet)
MR2520402

Zentralblatt MATH identifier
1225.55004

Subjects
Primary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) 55T20: Eilenberg-Moore spectral sequences [See also 57T35]

Keywords
Eilenberg–Moore spectral sequence

Citation

Shamir, Shoham. Cellular approximations and the Eilenberg–Moore spectral sequence. Algebr. Geom. Topol. 9 (2009), no. 3, 1309--1340. doi:10.2140/agt.2009.9.1309. https://projecteuclid.org/euclid.agt/1513797031


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