The Hopf ring for $P(n)$

Douglas C. Ravenel, W. Stephen Wilson
1996 Canadian Journal of Mathematics - Journal Canadien de Mathematiques  
We show that E * (P (n) * ), the E-homology of the Ω-spectrum for P (n), is an E * free Hopf ring for E a complex oriented theory with In sent to 0. This covers the cases P (q) * (P (n) * ) and K(q) * (P (n) * ), q ≥ n. The generators of the Hopf ring are those necessary for the stable result. The motivation for this paper is to show that P (n) satisfies all of the conditions for the machinery of unstable cohomology operations set up in [BJW95] . This can then be used to produce splittings
more » ... uce splittings analogous to those for BP done in [Wil75] .
doi:10.4153/cjm-1996-054-2 fatcat:o7jzre3mpvce5gahwu767b5naa