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About homotopy classes of non-singular vector fields on the three-sphere

Emmanuel Dufraine
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Abstract

Generically, the set of points along which two non-singular vector fields on the three-sphere are positively (resp. negatively) collinear form a link. We prove that the two vector fields are homotopic if and only if the linking number of those links is zero. We use this criterion to give a new proof of a result of Yano: every non-singular vector field on the three-sphere is homotopic to a non-singular Morse-Smale vector field.

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Emmanuel Dufraine. 2003-03-25. About homotopy classes of non-singular vector fields on the three-sphere. https://arxiv.org/abs/math/0303315

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