2 problems

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Existence of blow-away vector fields for arbitrary singular loci
Let $G:({\mathbb R}^{m},0)\to({\mathbb R}^{p},0)$ be a nice analytic map germ, and let ${\rm Sing}\,G$ denote its singular locus. A blow-away vector field tangent to…
Conjectureopensingularity-theory sphere-fibrationsarXiv posted 2 days ago
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Nonexistence of other 7-dimensional regular Riemannian foliations on the 15-sphere
Nonexistence conjecture. There are no $7$ -dimensional regular Riemannian foliations on $S^{15}$ other than the Hopf fibration
Conjectureopendifferential-geometry riemannian-foliations sphere-fibrationsarXiv posted 2 days ago

Existence of blow-away vector fields for arbitrary singular loci