Abstract
We compute the Brown-Peterson cohomology of QX, the free infinite loop-space on X, when X is a space whose Morava K-theory is flat over its BP-cohomology, in particular a space whose Morava K-theory is concentrated in even degrees. Our computation is in terms of a destabilization functor for BP-cohomology. We also show that for such X, the Morava K-homology of QX is a free commutative algebra.
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