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On two results of Singhof

Augustin-Liviu Mare (1997)

Commentationes Mathematicae Universitatis Carolinae

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 𝒜 -category (cf. [14]).

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