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PHANTOM MAPS AND THE TOWERS WHICH DETERMINE THEM

Published online by Cambridge University Press:  01 June 1997

C. A. McGIBBON  and
RICHARD STEINER
C. A. McGIBBON
Affiliation:
Department of Mathematics, Wayne State University, Detroit, Michigan 48202, USA. E-mail: mcgibbon@math.wayne.edu
RICHARD STEINER
Affiliation:
Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW. E-mail: rjs@maths.gla.ac.uk
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Abstract

Let X and Y be pointed spaces. A phantom map from X to Y is a map whose restriction to any finite skeleton of X is null-homotopic. Let Ph (X, Y) denote the set of homotopy classes of phantom maps from X to Y. As a pointed set it is isomorphic to the lim1 term of the tower of groups

formula here

where Y(n) denotes the Postnikov approximation of Y through dimension n. The homomorphisms in this tower are induced by the projections ΩY(n)← ΩY(n+1)). The groups in this tower are not abelian in general; however they do have some nice algebraic properties.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 55 , Issue 3 , June 1997 , pp. 601 - 608
Copyright
The London Mathematical Society 1997

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