Equivariant critical point theory and ideal-valued cohomological index (Q1343892)

The author develops an equivariant critical point theory for differentiable \(G\)-functions on a Banach \(G\)-manifold, where \(G\) is a compact Lie group. Instead of using \(G\)-Lyusternik-Shnirel'man category, he uses the ideal-valued cohomology index with respect to \(h^*\), which is a generalized \(G\)-cohomology theory, continuous and multiplicative with unit. He obtains several results providing lower bounds for the number of critical orbits and critical values of a map \(f: M\to \mathbb{R}\). Finally, as a consequence of the main results, he gets a lot more information about \(K\) (\(K\) the set of critical points of \(f\)) than those obtained by using Lyusternik-Shnirel'man category. The paper is quite clear and well organized.