Essential category weight and phantom maps

Abstract

The purpose of this paper is to study the relationship between maps with infinite essential category weight and phantom maps (there is a brief summary of the main results on essential category weight in the appendix to this paper). It is not hard to see that any map with E(f) = oo is a phantom map. We give examples to show that the converse is not always true: there are phantom maps f with E(f) = 1. We also show that if ¦¸X is homotopy equivalent to a finite dimensional CW complex then every phantom map f: X¡ªY has E(f) =¡Þ. We are able to adapt many of the results of the theory of phantom maps to give us results about maps with E(f) = ¡Þ. Finally, we use the connections between essential category weight and phantom maps to answer a question (asked by McGibbon) about phantom maps.KeywordsSpectral SequenceCohomology ClassFinite TypeCategory WeightAbelian Group StructureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.