The homotopy type of the space of gradient vector fields on the two-dimensional disc (Q2902682)
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scientific article; zbMATH DE number 6069865
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The homotopy type of the space of gradient vector fields on the two-dimensional disc |
scientific article; zbMATH DE number 6069865 |
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22 August 2012
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homotopy type
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gradient vector fields
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The homotopy type of the space of gradient vector fields on the two-dimensional disc (English)
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\textit{A. Parusiński} in [Stud. Math. 96, No. 1, 73--80 (1990; Zbl 0714.57015)] proved that if two gradient vector fields on the unit disc \(D^n\) and non-vanishing in \(S^{n-1}\) are homotopic, then they are gradient homotopic.NEWLINENEWLINEConsider the inclusion map of the space of gradient vector fields into the space of all vector fields on \(D^n\), non-vanishing in \(S^{n-1}\). The authors prove a version of the theorem of Parusinski, restricted to the two dimensional case, but improve the result, proving that the inclusion is a homotopy equivalence.
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0.8042398691177368
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0.7919245958328247
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