Classification of homotopy classes of equivariant gradient maps

E. N. Dancer ¹   ; K. G/eba ²   ; S. M. Rybicki ³

¹ School of Mathematics Sydney University Sydney, NSW 2006 Australia
² Faculty of Technical Physics and Applied Mathematics Technical University of Gdańsk Narutowicza 11-12 PL-80-952 Gdańsk, Poland
³ Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12-18 PL-87-100 Toruń, Poland

Fundamenta Mathematicae, Tome 185 (2005) no. 1, pp. 1-18

Résumé

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

Détail

DOI : 10.4064/fm185-1-1

Mots-clés : orthogonal representation compact lie group unit sphere disc respectively rightarrow mathbb g invariant map g equivariant gradient map nabla rightarrow said admissible provided nabla cap emptyset classify homotopy classes admissible g equivariant gradient maps nabla rightarrow setminus