G-invariante Morse-Funktionen. (G-invariant Morse functions) (Q1120164)

For compact G-manifolds (G is a compact Lie group) a special class of invariant Morse functions is introduced, which is shown to be dense (hence nonempty) in the space of invariant Morse functions with respect to the \({\mathcal C}^ 1\)-topology. It is proved that if f is a special Morse function on M then M is homotopy equivalent to a G-CW complex the equivariant \(\lambda\)-cells of which correspond to the critical orbits of f with index \(\lambda\). Applications deal with the Euler number of the fixed point set of the G action and Morse inequalities in the equivariant homology theory.