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$\DeclareMathOperator\Sp{Sp}\DeclareMathOperator\cat{cat}$The Lusternik–Schnirelmann category of the Lie groups $\Sp(n)$. Since $\Sp(1) = S^3$, $\cat(\Sp(1)) = 1$. In the 1960s, P. Schweitzer proved that $\cat(\Sp(2)) = 3$. Based on this, a folklore conjecture emerged that in general $\cat(\Sp(n)) = 2n-1$. In 2001, it was proved that $\cat(\Sp(3)) = 5$, so maybe it's true?