"New relationships among loopspaces, symmetric products, and Eilenberg MacLane spaces"
Nicholas J. Kuhn
AMS classification number: 55P42
Mathematics Department
University of Virginia
Charlottesville, VA 22903
njk4x@virginia.edu
This is a revised version of the 1996 preprint "New cohomological relationships among loopspaces, symmetric products, and Eilenberg MacLane spaces". The paper studies a bigraded family of finite spectra T(n,j), at p=2, which specialize to the dual Brown-Gitler spectra when n=1. One can take hocolimits of these as either j goes to infinity or n goes to infinity.
When one lets j go to infinity, one gets in cohomology A-modules, which are shown to be related to the cohomology of K(V,n)'s in the same way that the Carlsson modules are related to the cohomology of K(V,1)'s.
When one lets n go to infinity, one gets a filtration of HZ/2 that cohomologically looks like the mod 2 Whitehead conjecture filtration (a modified symmetric products of spheres filtration). A result new in the revision is that this IS the modified symmetric products of spheres filtration.
Also new in the revision is an appendix which relates my constructions to work of Arone-Mahowald, and Arone-Dwyer on the Goodwillie tower of spheres.