Algebraic and Geometric Topology 4 (2004), paper no. 36, pages 829-839.

Implications of the Ganea Condition

Norio Iwase, Donald Stanley and Jeffrey Strom

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.

Keywords. Lusternik-Schnirelmann category, Ganea conjecture, product formula, cone length

AMS subject classification. Primary: 55M30.

DOI: 10.2140/agt.2004.4.829

E-print: arXiv:math.AT/0410374

Submitted: 6 March 2004. Accepted: 30 September 2004. Published: 7 October 2004.

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Norio Iwase, Donald Stanley and Jeffrey Strom

Faculty of Mathematics, Kyushu University, Ropponmatsu 4-2-1
Fukuoka 810-8560, Japan

Department of Mathematics and Statistics, University of Regina, College West 307.14
Regina, Saskatchewan, Canada

Department of Mathematics, Western Michigan University, 1903 W. Michigan Ave
Kalamazoo, MI 49008, USA

Email: iwase@math.kyushu-u.ac.jp, stanley@math.uregina.ca, jeffrey.strom@wmich.edu

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