Abstract:For a compact connected semisimple Lie group $G$ we shall prove two results (both related with Singhof's paper [13]) on the Lusternik-Schnirelmann category of the adjoint orbits of $G$, respectively the 1-dimensional relative category of a maximal torus $T$ in $G$. The techniques will be classical, but we shall also apply some basic results concerning the so-called $\Cal A$-category (cf. [14]).
Keywords: Lusternik-Schnirelmann category, Lie groups, adjoint orbits
AMS Subject Classification: 55P50, 57T20, 57T15