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A counter example to Ganea's conjecture of least possible dimension

Resumo: The Lusternik-Schnirelmann category of a topological space X is a measure of the complexity of the space. When X is a manifold it gives a lower bound for the number of critical points of a smooth function on X. Ganea conjectured that when producting with a sphere the category of the space should increase by one. Around 10 years ago Iwase constructed a series of counterexamples, all of which had dimension at least 10. In this talk we construct a counterexample of dimension 7 and show that there are no 6 dimensional counterexamples. Other counterexamples arise from the instability of a Hopf invariant, however this example arises since a Hopf invariant becomes stably more divisible.
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