Classification of homotopy classes of equivariant gradient maps

E. N. Dancer, K. Gęba, and S. M. Rybicki. "Classification of homotopy classes of equivariant gradient maps." Fundamenta Mathematicae 185.1 (2005): 1-18. <http://eudml.org/doc/283144>.

@article{E2005,
abstract = {Let V be an orthogonal representation of a compact Lie group G and let S(V),D(V) be the unit sphere and disc of V, respectively. If F: V → ℝ is a G-invariant C¹-map then the G-equivariant gradient C⁰-map ∇F: V → V is said to be admissible provided that $(∇F)^\{-1\}(0) ∩ S(V) = ∅$. We classify the homotopy classes of admissible G-equivariant gradient maps ∇F: (D(V),S(V)) → (V,V∖0).},
author = {E. N. Dancer, K. Gęba, S. M. Rybicki},
journal = {Fundamenta Mathematicae},
keywords = {equivariant degree; gradient equivariant homotopy classes; Burnside ring; Riemannian manifolds; finite-dimensional orthogonal representation; compact Lie groups},
language = {eng},
number = {1},
pages = {1-18},
title = {Classification of homotopy classes of equivariant gradient maps},
url = {http://eudml.org/doc/283144},
volume = {185},
year = {2005},
}

TY - JOUR
AU - E. N. Dancer
AU - K. Gęba
AU - S. M. Rybicki
TI - Classification of homotopy classes of equivariant gradient maps
JO - Fundamenta Mathematicae
PY - 2005
VL - 185
IS - 1
SP - 1
EP - 18
AB - Let V be an orthogonal representation of a compact Lie group G and let S(V),D(V) be the unit sphere and disc of V, respectively. If F: V → ℝ is a G-invariant C¹-map then the G-equivariant gradient C⁰-map ∇F: V → V is said to be admissible provided that $(∇F)^{-1}(0) ∩ S(V) = ∅$. We classify the homotopy classes of admissible G-equivariant gradient maps ∇F: (D(V),S(V)) → (V,V∖0).
LA - eng
KW - equivariant degree; gradient equivariant homotopy classes; Burnside ring; Riemannian manifolds; finite-dimensional orthogonal representation; compact Lie groups
UR - http://eudml.org/doc/283144
ER -