An upper bound for the Lusternik-Schnirelmann category of the symplectic   group
  We prove that the LS category of the symplectic group $Sp(n)$ is bounded above by $\binom{n+1}{2}$. This is achieved by computing the number of critical levels of a height function. 
E. Mac\'ias-Virg\'os, M. J. Pereira-S\'aez
math.AT