Abstract
A 7-dimensional CW-complex having LusternikâSchnirelmann 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 LusternikâSchnirelmann category of spaces.
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