Stable Splittings and the Diagonal


Nicholas J. Kuhn                                  
Department of Mathematics, University of Virginia, Charlottesville, VA 22903
njk4x@virginia.edu


AMS classification numbers: Primary 55P35;  Secondary 55P42

Many approximations to function spaces admit natural stable splittings, with a typical example being the stable splitting of a space C_d(X) approximating Omega^d Sigma^d X. With an eye towards understanding cup products in the cohomology of such function spaces, we describe how the diagonal interacts with the stable splitting. The description involves group theoretic transfers. 

In an appendix independent of the rest of the paper, we use ideas from Goodwillie calculus to show that such natural stable splittings are unique, and discuss three different constructions showing their existence.