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Journal of the London Mathematical Society 2000 61(1):93-109; doi:10.1112/S0024610799008340
© 2000 by London Mathematical Society
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© The London Mathematical Society

The BP<N> Cohomology of Elementary Abelian Groups

N. P. Strickland

Trinity College Cambridge CB2 1TQ

Received 12 February 1998. Revision received 27 July 1998.

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≤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.


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