THE CONE LENGTH OF A PRODUCT OF CO-H-SPACES AND A PROBLEM OF GANEA

Abstract

It is proved that the cone length or strong category of a product of two co-H-spaces is less than or equal to two. This yields the following positive solution to a problem of Ganea. Let α ∈ π2p(S3) be an element of order p, p a prime [ges ] 3, and let X(p) = S3∪αe2p+1. Then X(p) × X(p) is the mapping cone of some map φ : Y → Z where Z is a suspension.