The complex oriented cohomology of extended powers
Annales de l'Institut Fourier, Volume 48 (1998) no. 2, p. 517-534

We examine the behaviour of a complex oriented cohomology theory G * (-) on D p (X), the C p -extended power of a space X, seeking a description of G * (D p (X)) in terms of the cohomology G * (X). We give descriptions for the particular cases of Morava K-theory K(n) for any space X and for complex cobordism MU, the Brown-Peterson theories BP and any Landweber exact theory for a wide class of spaces.

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.

@article{AIF_1998__48_2_517_0,
     author = {Hunton, John Robert},
     title = {The complex oriented cohomology of extended powers},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {48},
     number = {2},
     year = {1998},
     pages = {517-534},
     doi = {10.5802/aif.1627},
     zbl = {0899.55019},
     mrnumber = {99c:55017},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1998__48_2_517_0}
}
Hunton, John Robert. The complex oriented cohomology of extended powers. Annales de l'Institut Fourier, Volume 48 (1998) no. 2, pp. 517-534. doi : 10.5802/aif.1627. http://www.numdam.org/item/AIF_1998__48_2_517_0/

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