Comptes Rendus
no. 9-10
Homological Algebra/Topology
Wilson spaces and homological algebra for coalgebraic modules
[Les espaces de Wilson et l'algèbre homologique pour les modules cogèbriques]

Présenté par : Christophe Soulé

Takuji Kashiwabara1
1 Institut Fourier, Université de Grenoble I, UMR5582 CNRS, BP 74, 38402 St Martin d'Hères, France
Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 491-493.

Dans cet article, nous montrons que les espaces de Wilson peuvent être utilisés pour remplacer les espaces de lacets infinis associés au spectre de Brown–Peterson dans le calcul des CTor, les dérivées à gauche du produit tensoriel généralisé définies par Hunton et Turner.

In an earlier work, Wilson spaces were used to compute certain CTor Hopf algebras. In this Note we show how one can replace a resolution by infinite loop spaces associated to the Brown–Peterson spectrum with a resolution by Wilson spaces.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.03.002

Takuji Kashiwabara 1

1 Institut Fourier, Université de Grenoble I, UMR5582 CNRS, BP 74, 38402 St Martin d'Hères, France 
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Takuji Kashiwabara. Wilson spaces and homological algebra for coalgebraic modules. Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 491-493. doi : 10.1016/j.crma.2010.03.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.03.002/

[1] J.M. Boardman; D.C. Johnson; W.S. Wilson Unstable operations in generalized cohomology, Handbook of Algebraic Topology, North-Holland, Amsterdam, 1995, pp. 687-828

[2] J.M. Boardman; W.S. Wilson Unstable splittings related to Brown–Peterson cohomology, Bellaterra, 1998 (Progr. Math.), Volume vol. 196, Birkhäuser, Basel (2001), pp. 35-45

[3] E.H. Brown; F.P. Peterson A spectrum whose Zp cohomology is the algebra of reduced p-th powers, Topology, Volume 5 (1966), pp. 149-154

[4] P.G. Goerss Hopf rings, Dieudonné modules and E∗(Ω2S3) (J.-P. Meyer; J. Morava; W.S. Wilson, eds.), Homotopy Invariant Algebraic Structures: A Conference in Honor of J. Michael Boardman, Contemp. Math., vol. 239, Amer. Math. Soc., Providence, RI, 1999, pp. 115-174

[5] M.J. Hopkins; J.R. Hunton On the structure of spaces representing a Landweber exact cohomology theory, Topology, Volume 34 (1995), pp. 29-36

[6] J.R. Hunton; P.R. Turner Coalgebraic algebra, J. Pure Appl. Algebra, Volume 129 (1998), pp. 297-313

[7] J.R. Hunton; P.R. Turner The homology of spaces representing exact pairs of homotopy functors, Topology, Volume 38 (1999), pp. 621-623

[8] D.C. Johnson; W.S. Wilson BP-operations and Morava's extraordinary K-theories, Math. Z., Volume 144 (1975), pp. 55-75

[9] T. Kashiwabara Homological algebra for coalgebraic modules and mod p K-theory of infinite loop spaces, K-Theory, Volume 21 (2000), pp. 387-417

[10] T. Kashiwabara; W.S. Wilson The Morava K-theory and Brown–Peterson cohomology of spaces related to BP, J. Math. Kyoto Univ., Volume 41 (2001) no. 1, pp. 43-95

[11] S. MacLane Homology, Die Grundlehren der mathematischen Wissenschaften, Bd. 114, Academic Press, Inc., Publishers, New York, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1963

[12] C.A. McGibbon Wilson spaces and stable splittings of BTr, Glasgow Math. J., Volume 36 (1994) no. 3, pp. 287-290

[13] W.S. Wilson The Ω-spectrum for Brown–Peterson cohomology, part I, Comment. Math. Helv., Volume 4 (1973), pp. 45-55

[14] W.S. Wilson The Ω-spectrum for Brown–Peterson cohomology, part II, Amer. J. Math., Volume 97 (1975), pp. 102-123

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