Geodesic
Lusternik–Schnirelmann category of products with half-smashes
Stanley, Don1 ; Strom, Jeff2
1Department of Mathematics and Statistics, University of Regina, Regina, SK, Canada
2Department of Mathematics, Western Michigan University, Kalamazoo, MI, United States
Algebraic and Geometric Topology, Tome 20 (2020) no. 1, pp. 439-450
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We show that for a fixed space X and any sufficiently highly connected space A ( conn(A) > dim(X) is more than enough), the Lusternik–Schnirelmann category of products with X is remarkably stable with respect to changes in the second variable:

Taking X = Sn leads to a closure property for the collections of spaces which do or do not satisfy the Ganea condition cat(Sn × A) = 1 + cat(A).

DOI : 10.2140/agt.2020.20.439
Classification : 55M30
Keywords: Lusternik–Schnirelmann category, half-smash, Ganea conjecture, Ganea condition, cartesian product, homotopy theory

Stanley, Don  1   ; Strom, Jeff  2

1 Department of Mathematics and Statistics, University of Regina, Regina, SK, Canada
2 Department of Mathematics, Western Michigan University, Kalamazoo, MI, United States 
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Stanley, Don; Strom, Jeff. Lusternik–Schnirelmann category of products with half-smashes. Algebraic and Geometric Topology, Tome 20 (2020) no. 1, pp. 439-450. doi: 10.2140/agt.2020.20.439

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