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Phantom maps and chromatic phantom maps
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 122, Number 2, April 2000
- pp. 275-293
- 10.1353/ajm.2000.0011
- Article
- Additional Information
In the first part, we determine conditions on spectra X and Y under which either every map from X to Y is phantom, or no nonzero maps are. We also address the question of whether such all or nothing behavior is preserved when X is replaced with V Λ X for V finite. In the second part, we introduce chromatic phantom maps. A map is n-phantom if it is null when restricted to finite spectra of type at least n. We define divisibility and finite type conditions which are suitable for studying n-phantom maps. We show that the duality functor Wn-1 defined by Mahowald and Rezk is the analog of Brown-Comenetz duality for chromatic phantom maps, and give conditions under which the natural map Y → W2n-1Y is an isomorphism.