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

Annales Polonici Mathematici (1992)

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

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topDanuta 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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