Geodesic
Cellular approximations and the Eilenberg–Moore spectral sequence
Shamir, Shoham1
1School of Mathematics and Statistics, The University of Sheffield, Sheffield, S3 7RH, UK
Algebraic and Geometric Topology, Tome 9 (2009) no. 3, pp. 1309-1340
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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.

DOI : 10.2140/agt.2009.9.1309
Keywords: Eilenberg–Moore spectral sequence

Shamir, Shoham  1

1 School of Mathematics and Statistics, The University of Sheffield, Sheffield, S3 7RH, UK 
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Shamir, Shoham. Cellular approximations and the Eilenberg–Moore spectral sequence. Algebraic and Geometric Topology, Tome 9 (2009) no. 3, pp. 1309-1340. doi: 10.2140/agt.2009.9.1309

[1] A K Bousfield, The localization of spectra with respect to homology, Topology 18 (1979) 257

[2] W Chachólski, On the functors $CW_A$ and $P_A$, Duke Math. J. 84 (1996) 599

[3] E Dror Farjoun, Cellular spaces, null spaces and homotopy localization, Lecture Notes in Math. 1622, Springer (1996)

[4] W G Dwyer, Strong convergence of the Eilenberg–Moore spectral sequence, Topology 13 (1974) 255

[5] W G Dwyer, Exotic convergence of the Eilenberg–Moore spectral sequence, Illinois J. Math. 19 (1975) 607

[6] W G Dwyer, J P C Greenlees, Complete modules and torsion modules, Amer. J. Math. 124 (2002) 199

[7] W G Dwyer, J P C Greenlees, S Iyengar, Duality in algebra and topology, Adv. Math. 200 (2006) 357

[8] W G Dwyer, J P C Greenlees, S Iyengar, Finiteness in derived categories of local rings, Comment. Math. Helv. 81 (2006) 383

[9] W G Dwyer, C W Wilkerson, The fundamental group of a $p$–compact group, to appear in Bull. Lond. Math. Soc.

[10] A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, Math. Surveys and Monogr. 47, Amer. Math. Soc. (1997)

[11] P Hilton, G Mislin, J Roitberg, Localization of nilpotent groups and spaces, North-Holland Math. Stud. 15, North-Holland (1975)

[12] P S Hirschhorn, Model categories and their localizations, Math. Surveys and Monogr. 99, Amer. Math. Soc. (2003)

[13] I Kriz, Morava $K$–theory of classifying spaces: some calculations, Topology 36 (1997) 1247

[14] M Rothenberg, N E Steenrod, The cohomology of classifying spaces of $H$–spaces, Bull. Amer. Math. Soc. 71 (1965) 872

[15] S Schwede, B Shipley, Stable model categories are categories of modules, Topology 42 (2003) 103

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