Phantom Maps and Chromatic Phantom Maps
نویسندگان
چکیده
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 behaviour is preserved when X is replaced with V ∧ 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 → W 2 n−1Y is an isomorphism.
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ar X iv : m at h / 98 11 02 7 v 1 [ m at h . A T ] 5 N ov 1 99 8 PHANTOM MAPS AND CHROMATIC PHANTOM MAPS
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 behaviour is preserved when X is replaced with V ∧ 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...
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