A minimum dimensional counterexample to Ganea's conjecture |
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| Authors: | Donald Stanley |
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| Affiliation: | a Department of Mathematics and Statistics, University of Regina, 3737 Wascana Pkwy, Regina, SK, Canada, S4S 0A2
b Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Av. Universidad #940, Col. Ciudad Universitaria, 20131 Aguascalientes, Ags, Mexico |
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| Abstract: | A 7-dimensional CW-complex having Lusternik-Schnirelmann category equal to 2 is constructed. Using a divisibility phenomenon for Hopf invariants, it is proved that the Cartesian product of the constructed complex with a sphere of sufficiently large dimension also has category 2. This space hence constitutes the minimum dimensional known counterexample to Ganea's conjecture on the Lusternik-Schnirelmann category of spaces. |
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| Keywords: | Lusternik-Schnirelmann category Ganea's conjecture |
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