Homological Algebra/Topology
Wilson spaces and homological algebra for coalgebraic modules
Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 491-493

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2010.03.002

Kashiwabara, Takuji 1

1 Institut Fourier, Université de Grenoble I, UMR5582 CNRS, BP 74, 38402 St Martin d'Hères, France
@article{CRMATH_2010__348_9-10_491_0,
     author = {Kashiwabara, Takuji},
     title = {Wilson spaces and homological algebra for coalgebraic modules},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {491--493},
     year = {2010},
     publisher = {Elsevier},
     volume = {348},
     number = {9-10},
     doi = {10.1016/j.crma.2010.03.002},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.crma.2010.03.002/}
}
TY  - JOUR
AU  - Kashiwabara, Takuji
TI  - Wilson spaces and homological algebra for coalgebraic modules
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 491
EP  - 493
VL  - 348
IS  - 9-10
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.crma.2010.03.002/
DO  - 10.1016/j.crma.2010.03.002
LA  - en
ID  - CRMATH_2010__348_9-10_491_0
ER  - 
%0 Journal Article
%A Kashiwabara, Takuji
%T Wilson spaces and homological algebra for coalgebraic modules
%J Comptes Rendus. Mathématique
%D 2010
%P 491-493
%V 348
%N 9-10
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.crma.2010.03.002/
%R 10.1016/j.crma.2010.03.002
%G en
%F CRMATH_2010__348_9-10_491_0
Kashiwabara, Takuji. 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

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

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

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

[4] Goerss, P.G. Hopf rings, Dieudonné modules and E(Ω2S3) (Meyer, J.-P.; Morava, J.; Wilson, W.S., 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] Hopkins, M.J.; Hunton, J.R. On the structure of spaces representing a Landweber exact cohomology theory, Topology, Volume 34 (1995), pp. 29-36

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

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

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

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

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

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

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

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

Cited by Sources: