Abstract: Can any embedded 3-sphere be realized as a leaf of a codimension two foliation of \({\mathbb{R}}^{5}\)? Does there exist a submersion \(\varPhi: {\mathbb{R}}^{3} \rightarrow {\mathbb{R}}^{2}\) with a knotted fibre Φ −1(0)? For any link L, does there exist a non vanishing Morse-Smale flow in \({\mathbb{R}}^{3}\) whose whole set of periodic trajectories is given by L? These apparently unrelated problems can be addressed using the theory of integrable embeddings recently introduced by Gilbert Hector and the author. In this paper I will provide ...
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Pure mathematics