Relative phantom maps

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...

Phantom Maps and Forgetable Maps

In this note, we attack a question posed ten years ago by Tsukiyama about the injectivity of the socalled Forgetable map. We show that we can insert the Forgetable map in an exact sequence and that the problem can be reduced to the computation of the sequence which turns out unexpectedly to be related to the phantom map problem and the famous Halperin conjecture in rational homotopy theory.

Relative Compactness and Product Stable Quotient Maps

Equivariant Phantom Maps

A successful generalization of phantom map theory to the equivariant case for all compact Lie groups is obtained in this paper. One of the key observations is the discovery of the fact that homotopy fiber of equivariant completion splits as product of equivariant Eilenberg-Maclane spaces which seems impossible at first sight by the example of Triantafillou[19].

Higher Order Phantom Maps

For each ordinal number α, we define phantom maps of order α. We construct universal phantom maps out ofX with order α, and show that under easily verifiable conditions, every one of these universal phantom maps is essential. Math. Subject Classifications: 55P05, 55S36