Recherche et téléchargement d’archives de revues mathématiques numérisées

  
 
  Table des matières de ce fascicule | Article précédent | Article suivant
Hunton, John Robert
The complex oriented cohomology of extended powers. Annales de l'institut Fourier, 48 no. 2 (1998), p. 517-534
Texte intégral djvu | pdf | Analyses MR 99c:55017 | Zbl 0899.55019

URL stable: http://www.numdam.org/item?id=AIF_1998__48_2_517_0

Voir cet article sur le site de l'éditeur

Résumé

Nous étudions le comportement d'une théorie à orientation complexe $G^*(-)$ sur un espace du type $ D_p(X)$, la puissance $C_p$-étendue d'un espace $X$, à la recherche d'une description de $G^*(D_p(X))$ en fonction de $G^*(X)$. Nous donnons une telle description dans le cas particulier des $K$-théories de Morava $K(n)$ (pour $X$ espace quelconque) et dans le cas du cobordisme complexe $MU$, de la théorie de Brown-Peterson BP ou de n'importe quelle théorie Landweber-exacte, pour $X$ décrivant une vaste classe d'espaces.

Bibliographie

[1] A.J. BAKER and J.R. HUNTON, Continuous Morava K-theory and the geometry of the In-adic tower, Math. Scand., 75 (1994), 67-81.
Article |  MR 96a:55009 |  Zbl 0828.55003
[2] A.J. BAKER and U. WÜRGLER, Bockstein operations in Morava K-theories, Forum Math., 3 (1991), 543-560.  MR 92i:55009 |  Zbl 0751.55002
[3] R. BRUNER, J.P. MAY, J.E. MCCLURE and M. STEINBERGER, H∞ ring spectra and their applications, Springer Lecture Notes in Math., vol. 1176 (1986).  MR 88e:55001 |  Zbl 0585.55016
[4] A.D. ELMENDORF, I. KRIZ, M.A. MANDELL, J.P. MAY, Modern foundations for stable homotopy theory, Handbook of Algebraic Topology, editor I. M. James, (1995) Elsevier North-Holland.  MR 97d:55016 |  Zbl 0865.55007
[5] M.J. HOPKINS and J.R. HUNTON, On the structure of spaces representing a Landweber exact cohomology theory, Topology, 34 (1995), 29-36.  MR 95k:55009 |  Zbl 0862.55005
[6] M. HOVEY, Bousfield Localisation functors and Hopkins' chromatic splitting conjecture, Proceedings of the Čech Centennial Homotopy conference, June 1993, American Mathematical Society Contemporary Mathematics Series, editors Mila Cenkl and Haynes Miller, 181 (1995), 225-250.  Zbl 0830.55004
[7] M. HOVEY and H. SADOFSKI, Invertible spectra in the E(n) local stable homotopy category, to appear, Journal of the London Mathematical Society.  Zbl 0947.55013
[8] M. HOVEY and N. STRICKLAND, Morava K-theories and localisation, preprint.  Zbl 0929.55010
[9] J.R. HUNTON, The Morava K-theory of wreath products, Math. Proc. Camb. Phil. Soc., 107 (1990), 309-318.  MR 91a:55004 |  Zbl 0705.55009
[10] J.R. HUNTON, Detruncating Morava K-theory, Proc. Adams Memorial Symposium, LMS Lecture notes series, C.U.P., 176 (1992) 35-43.  MR 94k:55010 |  Zbl 0751.55003
[11] J.R. HUNTON and P.R. TURNER, An exactness theorem for the homology of representing spaces, preprint.
[12] T. KASHIWABARA, On Brown-Peterson cohomology of QX, preprint.  Zbl 0985.55006
[13] P.S. LANDWEBER, Homological properties of comodules over MU*(MU) and BP*(BP), Amer. J. Math., 98 (1976), 591-610.  MR 54 #11311 |  Zbl 0355.55007
[14] D. LAZARD, Autour de la platitude, Bull. Soc. Math. France, 97 (1969), 81-128.
Numdam |  MR 40 #7310 |  Zbl 0174.33301
[15] I.J. LEARY, On the integral cohomology of wreath products, to appear, J. Algebra.  Zbl 0893.55009
[16] L.G. LEWIS, Jr., J.P. MAY and M. STEINBERGER, Equivariant stable homotopy theory, Springer Lecture Notes in Math., vol. 1213 (1986).  MR 88e:55002 |  Zbl 0611.55001
[17] J.E. MCCLURE and V.P. SNAITH, On the K-theory of the extended power construction, Math. Proc. Camb. Phil. Soc., 92 (1982), 263-274.  MR 83j:55004 |  Zbl 0508.55021
[18] J. MILNOR, The Steenrod algebra and its dual, Ann. Math., 67 (1958), 150-171.  MR 20 #6092 |  Zbl 0080.38003
[19] M. NAKAOKA, Homology of the infinite symmetric group, Ann. Math., 73 (1961), 229-257.  MR 24 #A1721 |  Zbl 0099.25301
[20] D.C. RAVENEL and W.S. WILSON, The Hopf ring for complex cobordism, Journal of Pure and Applied Algebra, 9 (1977), 241-280.  MR 56 #6644 |  Zbl 0373.57020
[21] D.C. RAVENEL and W.S. WILSON, The Morava K-theories of Eilenberg-MacLane spaces and the Conner-Floyd conjecture, Amer. J. Math., 102 (1980), 691-748.  MR 81i:55005 |  Zbl 0466.55007
[22] D.C. RAVENEL, W.S. WILSON and N. YAGITA, Brown-Peterson cohomology from Morava K-theory, to appear, Journal of K-theory.  Zbl 0912.55002
[23] V.P. SNAITH, A stable decomposition of ΩnΣnX, J. London Math. Soc., 7 (1974), 577-583.  MR 49 #3918 |  Zbl 0275.55019
[24] D. TAMAKI, Ph. D. thesis, University of Rochester.
[25] U. WÜRGLER, On products in a family of cohomology theories associated to the invariant prime ideals of π*(BP), Comment. Math. Helv., 52 (1977), 457-481.  MR 57 #17624 |  Zbl 0379.55002
[26] N. YAGITA, On the Steenrod algebra of Morava K-theory, J. London Math. Soc., (2) 22 (1980), 423-438.  MR 82f:55027 |  Zbl 0453.55013
Copyright Cellule MathDoc 2013 | Crédit | Plan du site