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The complex oriented cohomology of extended powers

John Robert Hunton (1998)

Annales de l'institut Fourier

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 M U , the Brown-Peterson theories BP and any Landweber exact theory for a wide class of spaces.

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