Classification of homotopy classes of equivariant gradient maps

Volume 185 / 2005

E. N. Dancer, K. G/eba, S. M. Rybicki Fundamenta Mathematicae 185 (2005), 1-18 MSC: 47H11, 55P91. DOI: 10.4064/fm185-1-1


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 $\nabla F : (D(V),S(V)) \rightarrow (V, V\setminus \{0\})$.


  • E. N. DancerSchool of Mathematics
    Sydney University
    Sydney, NSW 2006
  • K. G/ebaFaculty of Technical Physics
    and Applied Mathematics
    Technical University of Gdańsk
    Narutowicza 11-12
    PL-80-952 Gdańsk, Poland
  • S. M. RybickiFaculty of Mathematics
    and Computer Science
    Nicolaus Copernicus University
    Chopina 12-18
    PL-87-100 Toruń, Poland

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