Cellular approximations and the Eilenberg–Moore spectral sequence

Shamir, Shoham

doi:10.2140/agt.2009.9.1309

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Cellular approximations and the Eilenberg–Moore spectral sequence

Shoham Shamir

Algebraic & Geometric Topology 9 (2009) 1309–1340

DOI: 10.2140/agt.2009.9.1309

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.

Keywords

Eilenberg–Moore spectral sequence

Mathematical Subject Classification 2000

Primary: 55P43, 55T20

References

Publication

Received: 13 December 2007

Revised: 17 April 2009

Accepted: 19 April 2009

Published: 5 July 2009

Authors

Shoham Shamir
School of Mathematics and Statistics The University of Sheffield Sheffield, S3 7RH UK

Volume 9, issue 3 (2009)