Implications of the Ganea condition

Iwase, Norio; Stanley, Donald; Strom, Jeffrey

doi:10.2140/agt.2004.4.829

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Implications of the Ganea condition

Norio Iwase, Donald Stanley and Jeffrey Strom

Algebraic & Geometric Topology 4 (2004) 829–839

DOI: 10.2140/agt.2004.4.829

arXiv: math.AT/0410374

Abstract

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

Mathematical Subject Classification 2000

Primary: 55M30

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Publication

Received: 6 March 2004

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

Volume 4, issue 2 (2004)