The Gray filtration on phantom maps

• Autorzy: Lê Minh Hà , Jeffrey Strom
• Języki publikacji: EN

Abstrakty

EN

This paper is a study of the Gray index of phantom maps. We give a new, tower theoretic, definition of the Gray index, which allows us to study the naturality properties of the Gray index in some detail.
McGibbon and Roitberg have shown that if f* is surjective on rational cohomology, then the induced map on phantom sets is also surjective. We show that if f* is surjective just in dimension k, then f induces a surjection on a certain subquotient of the phantom set. If the condition holds for all k, we recover McGibbon and Roitberg's theorem. There is a dual result, and a theorem on phantom maps into spheres which holds one dimension at a time as well.
Finally, we examine the set of phantom maps whose Gray index is infinite. The main theorem is a partial verification of our conjecture that if X and Y are nilpotent and of finite type, then every phantom map f: X → Y must have finite index.

Kategorie tematyczne

• 55P30: Eckmann-Hilton duality
• 55S37: Classification of mappings
• 20J05: Homological methods in group theory
• 55P62: Rational homotopy theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 167
• Numer: 3
• Strony: 251-268

Daty

wydano

2001

Twórcy

autor

Lê Minh Hà

• Department of Mathematics, University of Toledo, Toledo, OH 43606, U.S.A.

autor

Jeffrey Strom

• Department of Mathematics, Dartmouth College, Hanover, NH 03755, U.S.A.

Identyfikatory

DOI

10.4064/fm167-3-3