The complex oriented cohomology of extended powers

Hunton, John Robert

Annales de l'Institut Fourier, Tome 48 (1998) no. 2, pp. 517-534.

Nous étudions le comportement d’une théorie à orientation complexe $G^{*}(-)$ sur un espace du type $D_p\left(X\right)$, la puissance $C_p$-étendue d’un espace $X$, à la recherche d’une description de $G^{*}(D_p\left(X\right))$ en fonction de $G^{*}\left(X\right)$. Nous donnons une telle description dans le cas particulier des $K$-théories de Morava $K\left(n\right)$ (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.

We examine the behaviour of a complex oriented cohomology theory $G^{*}(-)$ on $D_p\left(X\right)$, the $C_p$-extended power of a space $X$, seeking a description of $G^{*}(D_p\left(X\right))$ in terms of the cohomology $G^{*}\left(X\right)$. We give descriptions for the particular cases of Morava $K$-theory $K\left(n\right)$ 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.

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