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

Danuta Rozpłoch-Nowakowska

ArticleOriginal scientific text

Title

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

Authors ¹

Affiliations

Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Abstract

A lower estimate is proved for the number of critical orbits and critical values of a G-invariant C¹ function

f : S^{n} \to 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.

Keywords

ENG

join, group actions, Borsuk's Antipodal Theorem, critical points

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Title

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

Affiliations

Abstract

Keywords

Bibliography