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Classification of homotopy classes of equivariant gradient maps

E. N. Dancer; K. Gęba; S. M. Rybicki — 2005

Fundamenta Mathematicae

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 ${(\nabla F)}^{- 1} (0) \cap S (V) = \emptyset$ . We classify the homotopy classes of admissible G-equivariant gradient maps ∇F: (D(V),S(V)) → (V,V∖0).

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