Geodesic
Implications of the Ganea condition
Iwase, Norio1 ; Stanley, Donald2 ; Strom, Jeffrey3
1Faculty of Mathematics, Kyushu University, Ropponmatsu 4-2-1, Fukuoka 810-8560, Japan
2Department of Mathematics and Statistics, University of Regina, College West 307.14, Regina, Saskatchewan, Canada
3Department of Mathematics, Western Michigan University, 1903 West Michigan Ave, Kalamazoo, MI 49008, USA
Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 829-839
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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.

DOI : 10.2140/agt.2004.4.829
Keywords: Lusternik–Schnirelmann category, Ganea conjecture, product formula, cone length

Iwase, Norio  1   ; Stanley, Donald  2   ; Strom, Jeffrey  3

1 Faculty of Mathematics, Kyushu University, Ropponmatsu 4-2-1, Fukuoka 810-8560, Japan
2 Department of Mathematics and Statistics, University of Regina, College West 307.14, Regina, Saskatchewan, Canada
3 Department of Mathematics, Western Michigan University, 1903 West Michigan Ave, Kalamazoo, MI 49008, USA 
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Iwase, Norio; Stanley, Donald; Strom, Jeffrey. Implications of the Ganea condition. Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 829-839. doi: 10.2140/agt.2004.4.829

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