Advanced Search

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.