In this paper we define three elements of a certain generalised cohomology ring
BP〈m, n〉* BVk.
Here m, n and k are non-negative integers
with k+m[les ]n+1, there
is a fixed prime p not exhibited in the notation, and Vk
is an elementary Abelian p-group of rank k. We show that these
elements are equal; this is striking, because the
three definitions are very different. The significance of our equation is not yet entirely
clear, but it makes contact with other work in the literature in a number of fascinating
ways.