There are many reasons for seeking to create a global database with which to record the outcomes of therapy for congenital heart disease. Such a database can function as a tool to support a variety of purposes:

(Volume 129 (2000), 263–275)

It is with very great regret that we record the death of one of the authors, Frank Peterson, shortly before the appearance of the paper. The Authors and Editor wish to express their great personal and professional respect for him.

The Dickson algebra Wn+1 of invariants in a polynomial algebra over [ ]2 is an unstable algebra over the mod 2 Steenrod algebra [Ascr ], or equivalently, over the Kudo–Araki–May algebra [Kscr ] of ‘lower’ operations. We prove that Wn+1 is a free unstable algebra on a certain cyclic module, modulo just one additional relation. To achieve this, we analyse the interplay of actions over [Ascr ] and [Kscr ] to characterize unstable cyclic modules with trivial action by the subalgebra [Ascr ]n−2 on a fundamental class in degree 2n – a. This involves a new family of left ideals [Iscr ]a in [Kscr ], which play the role filled by the ideals [Ascr ][Ascr ]n−2 in the Steenrod algebra.

We attack the conjecture that the only spherical classes in the homology of Q0S0 are Hopf invariant one and Kervaire invariant one elements. We do this by computing products in the E2-term of the unstable Adams spectral sequence converging to π∗(Q0S0), using results about the Dickson algebra and by studying the Lannes–Zarati homomorphism.

R. M. W. Wood has proved a conjecture we made about dimensions of A generators of H*(RP∞ × … × RP∞). In this note we give some of the consequences of this conjecture.

Some explicit formulae for the right coaction of A* on H*BO are given. As corollaries, closed formulae for χ(ξk) and other elements in A* are given.