Classification of homotopy classes of equivariant gradient maps
Volume 185 / 2005
Fundamenta Mathematicae 185 (2005), 1-18
MSC: 47H11, 55P91.
DOI: 10.4064/fm185-1-1
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 $F : V \rightarrow \mathbb R$ is a $G$-invariant $C^1$-map then the $G$-equivariant gradient $C^0$-map $\nabla F : V \rightarrow V$ 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 $\nabla F : (D(V),S(V)) \rightarrow (V, V\setminus \{0\})$.
