An effective criterion for the existence of a mass partition
We give an example of a space with the property that every orientable fibration with the fiber is rationally totally non-cohomologous to zero, while there exists a nontrivial derivation of the rational cohomology of of negative degree.
We explore connections between our previous paper [J. Reine Angew. Math. 604 (2007)], where we constructed spectra that interpolate between bu and Hℤ, and earlier work of Kuhn and Priddy on the Whitehead conjecture and of Rognes on the stable rank filtration in algebraic K-theory. We construct a "chain complex of spectra" that is a bu analogue of an auxiliary complex used by Kuhn-Priddy; we conjecture that this chain complex is "exact"; and we give some supporting evidence. We tie this to work of...