1School of Mathematics Sydney University Sydney, NSW 2006 Australia 2Faculty of Technical Physics and Applied Mathematics Technical University of Gdańsk Narutowicza 11-12 PL-80-952 Gdańsk, Poland 3Faculty 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
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 $\nabla F : (D(V),S(V))
\rightarrow (V, V\setminus \{0\})$.
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
Affiliations des auteurs :
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
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author = {E. N. Dancer and K. G/eba and S. M. Rybicki},
title = {Classification of homotopy classes
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E. N. Dancer; K. G/eba; S. M. Rybicki. Classification of homotopy classes
of equivariant gradient maps. Fundamenta Mathematicae, Tome 185 (2005) no. 1, pp. 1-18. doi: 10.4064/fm185-1-1
