|DAN CHRISTENSEN, Johns Hopkins University, Baltimore, Maryland 21218, USA|
|Phantom maps: all or nothing|
The general theme is to determine conditions on spectra X and Yunder which either every map from X to Y is phantom, or no non-zero maps are. I will also address the question of whether such all or nothing behaviour is preserved when X is smashed with a finite spectrum W. It turns out that there are close connections with the divisibility and rationality of the group [X,Y], and with Brown-Comenetz duality.
If there is time, I will discuss n-phantom maps, a chromatic analog of phantom maps, and use this concept to give another explanation of the results on phantom maps.
This is joint work with Mark Hovey and Sharon Hollander.