Article

Israel Journal of Mathematics

, Volume 58, Issue 2, pp 129-143

First online:

On phantom maps and a theorem of H. Miller

  • A. ZabrodskyAffiliated withInstitute of Mathematics, The Hebrew University of Jerusalem

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Abstract

A mapf:XY is a phantom map if any composition off with a map from a finite complex intoX is null homotopic. The proof of the Sullivan conjecture by H. Miller enables us to understand more deeply this phenomena. We prove, among other things, that any map from a space with finitely many non-vanishing homotopy groups into a finite complex is phantom and that any fibration over a 2-connected space with finitely many non-vanishing homotopy groups and with fiber a finite complex is trivial over each skeleton of the base.