Stable splittings and the diagonal (Q2752875)

Many approximations to function spaces admit natural stable splittings, with a typical example being the stable splitting of a space \(C_dX\) approximating \(\Omega^d\Sigma^dX\). With an eye towards understanding cup products in the cohomology of such function spaces, the author describes how the diagonal interacts with the stable splitting. The description involves group theoretic transfers. In an appendix independent of the rest of the paper, he uses ideas from Goodwillie calculus to show that such natural stable splittings are unique, and discusses three different constructions showing their existence.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00013].