| PHANTOM MAPS AND CHROMATIC PHANTOM MAPS (2007) | |||||||||||||||
Abstract | |||||||||||||||
| Abstract. In the rst 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 nite. In the second part, we introduce chromatic phantom maps. A map is n-phantom if it is null when restricted to nite spectra of type at least n. We dene divisibility and nite type conditions which are suitable for studying n-phantom maps. We show that the duality functor Wn 1 dened 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 | |||||||||||||||
Publication details | |||||||||||||||
| |||||||||||||||