An upper bound for the Lusternik-Schnirelmann category of the symplectic group (Q2845623)

The Lusternik-Schnirelmann category of a given class of compact Lie groups is, with few exceptions, unknown. This is the case of the \(n\)-th symplectic group \(Sp(n)\) for which, in the paper under review, the authors find an interesting upper bound, NEWLINE\[NEWLINE \text{cat}\, Sp(n)\leq \binom{n+1}{2}. NEWLINE\]NEWLINE This is deduced from a more general result by which the authors bound from above the Lusternik-Schnirelmann category of any compact Lie group \(G\) of orthogonal type in terms of an explicit description of the critical set of a very geometric and interesting height function \(h: G\to \mathbb{R}\).