CLASSIFICATION OF HOMOTOPY CLASSES OF EQUIVARIANT GRADIENT MAPS

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, respec-tively. 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}). 1