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

Danuta Rozpłoch-Nowakowska

Annales Polonici Mathematici (1992)

  • Volume: 56, Issue: 2, page 195-211
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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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 56.2 (1992): 195-211. <http://eudml.org/doc/262473>.

@article{DanutaRozpłoch1992,
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.},
author = {Danuta Rozpłoch-Nowakowska},
journal = {Annales Polonici Mathematici},
keywords = {join; group actions; Borsuk's Antipodal Theorem; critical points; -invariant function; number of critical orbits and critical values; Borsuk’s antipodal theorem for equivariant maps of joins of -sets},
language = {eng},
number = {2},
pages = {195-211},
title = {Equivariant maps of joins of finite G-sets and an application to critical point theory},
url = {http://eudml.org/doc/262473},
volume = {56},
year = {1992},
}

TY - JOUR
AU - Danuta Rozpłoch-Nowakowska
TI - Equivariant maps of joins of finite G-sets and an application to critical point theory
JO - Annales Polonici Mathematici
PY - 1992
VL - 56
IS - 2
SP - 195
EP - 211
AB - 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.
LA - eng
KW - join; group actions; Borsuk's Antipodal Theorem; critical points; -invariant function; number of critical orbits and critical values; Borsuk’s antipodal theorem for equivariant maps of joins of -sets
UR - http://eudml.org/doc/262473
ER -

References

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  12. [12] R. S. Palais, Critical point theory and the minimax principle, in: Proc. Sympos. Pure Math. 15, Amer. Math. Soc., 1970, 185-212. Zbl0212.28902
  13. [13] R. S. Palais, Lusternik-Schnirelmann theory on Banach manifolds, Topology 5 (1966), 115-132. Zbl0143.35203
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  16. [16] J. A. Wolf, Spaces of Constant Curvature, University of California, Berkeley, Calif., 1972. 

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