Equivariant maps of joins of finite G-sets and an application to critical point theory
Volume 56 / 1992
Annales Polonici Mathematici 56 (1992), 195-211
DOI: 10.4064/ap-56-2-195-211
Abstract
A lower estimate is proved for the number of critical orbits and critical values of a G-invariant C¹ function $f:S^n → ℝ$, where G is a finite nontrivial group acting freely and orthogonally on $ℝ^{n+1} \ {0}$. 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.
