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Equivariant maps of joins of finite G-sets and an application to critical point theory

Danuta Rozpłoch-Nowakowska (1992)

Annales Polonici Mathematici

A lower estimate is proved for the number of critical orbits and critical values of a G-invariant C¹ function f : S n , where G is a finite nontrivial group acting freely and orthogonally on n + 1 0 . Neither Morse theory nor the minimax method is applied. The proofs are based on a general version of Borsuk’s Antipodal Theorem for equivariant maps of joins of G-sets.

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