The BP-theory of 2-fold products of real projective spaces

Abstract

We study the Brown-Peterson (co)homology of a product of two real projective spaces via the Landweber short exact sequence. The image of the tensor product is well understood. Our contribution is to understand those elements not in the tensor product and to show how they behave under maps. The results are partially extended to the case where one of the factors is replaced by a $2^e$-torsion lens space.