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(X × A) = cat(X). Then there is a strict inequality cat(X × (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