Algebraic & Geometric Topology

Cellular approximations and the Eilenberg–Moore spectral sequence

Shoham Shamir

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Eilenberg–Moore spectral sequence


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.

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