Geodesic
Equivariant maps of joins of finite G-sets and an application to critical point theory
Annales Polonici Mathematici, Tome 56 (1991) no. 2, pp. 195-211.

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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.
DOI : 10.4064/ap-56-2-195-211
Keywords: join, group actions, Borsuk's Antipodal Theorem, critical points

Danuta Rozpłoch-Nowakowska 1

1 
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Danuta Rozpłoch-Nowakowska. Equivariant maps of joins of finite G-sets and an application to critical point theory. Annales Polonici Mathematici, Tome 56 (1991) no. 2, pp. 195-211. doi : 10.4064/ap-56-2-195-211. http://geodesic.mathdoc.fr/articles/10.4064/ap-56-2-195-211/

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