Geodesic
Gradient versus proper gradient homotopies
Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 61-76.

Voir la notice de l'article provenant de la source International Press of Boston

We compare the sets of homotopy classes of gradient and proper gradient vector fields in the plane. Namely, we show that gradient and proper gradient homotopy classifications are essentially different. We provide a complete description of the sets of homotopy classes of gradient maps from $\mathbb{R}^n$ to $\mathbb{R}^n$ and proper gradient maps from $\mathbb{R}^2$ to $\mathbb{R}^2$ with the Brouwer degree greater or equal to zero.
DOI : 10.4310/HHA.2021.v23.n1.a5
Classification : 55Q05, 55M25
Keywords: gradient map, proper map, homotopy 
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     title = {Gradient versus proper gradient homotopies},
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     pages = {61--76},
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     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n1.a5/}
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Piotr Bartłomiejczyk; Piotr Nowak-Przygodzki. Gradient versus proper gradient homotopies. Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 61-76. doi : 10.4310/HHA.2021.v23.n1.a5. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n1.a5/

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