Unstable homotopy theory 1 — The Johnson question.

The Johnson question. This says that if X is a space, and x is in BP_n (X), then x is not v_n torsion. My guess is that one should consider this question as a test case for whether there can be a really powerful analog of the Lannes theory of unstable algebras over the Steenrod algebra using BP instead. Such a theory has been constructed by Boardman, Johnson, and Wilson, but so far it has been unable to resolve this question.