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Implications of the Ganea Condition

Norio Iwase·Donald Stanley·Jeffrey Strom
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Abstract

Suppose the spaces X and X cross A have the same Lusternik-Schnirelmann category: cat(X cross A)= cat(X). Then there is a strict inequality cat(X cross (A halfsmash B)) < cat (X) + cat(A halfsmash B) for every space B, provided the connectivity of A is large enough (depending only on X). This is applied to give a partial verification of a conjecture of Iwase on the category of products of spaces with spheres.

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Norio Iwase, Donald Stanley, Jeffrey Strom. 2004-10-18. Implications of the Ganea Condition. https://doi.org/10.2140/agt.2004.4.829

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