The ${BP}$-theory of two-fold  products of projective spaces


Jes\'us Gonz\'alez
Departamento de Matem\'aticas
Centro de Investigaci\'on y de Estudios Avanzados del IPN
M\'exico City 07000
jesus@math.cinvestav.mx

W. Stephen Wilson
Department of Mathematics 
Johns Hopkins University 
Baltimore, Maryland 21218}
wsw@math.jhu.edu


We compute the BP (co)homology of the product of two
(stunted) projective spaces.  The behavior under maps
(particularly of the Tor term) is studied.  This is used
extensively by Kitchloo and Wilson in their work on
non-immersions.  Additional work with lens spaces is also
included.