#### Volume 4, issue 2 (2004)

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Implications of the Ganea condition

### Norio Iwase, Donald Stanley and Jeffrey Strom

Algebraic & Geometric Topology 4 (2004) 829–839
 arXiv: math.AT/0410374
##### Abstract

Suppose the spaces $X$ and $X×A$ have the same Lusternik–Schnirelmann category: $cat\left(X×A\right)=cat\left(X\right)$. Then there is a strict inequality $cat\left(X×\left(A⋊B\right)\right) 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.

##### Keywords
Lusternik–Schnirelmann category, Ganea conjecture, product formula, cone length
Primary: 55M30
##### Publication
Accepted: 30 September 2004
Published: 7 October 2004
##### Authors
 Norio Iwase Faculty of Mathematics Kyushu University Ropponmatsu 4-2-1 Fukuoka 810-8560 Japan Donald Stanley Department of Mathematics and Statistics University of Regina College West 307.14 Regina Saskatchewan Canada Jeffrey Strom Department of Mathematics Western Michigan University 1903 West Michigan Ave Kalamazoo MI 49008 USA