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.
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Strom, J. (2001). Essential category weight and phantom maps. In: Aguadé, J., Broto, C., Casacuberta, C. (eds) Cohomological Methods in Homotopy Theory. Progress in Mathematics, vol 196. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8312-2_25
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DOI: https://doi.org/10.1007/978-3-0348-8312-2_25
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9513-2
Online ISBN: 978-3-0348-8312-2
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