We prove that every germ of a smooth fibration of an odd-dimensional round sphere by great circles extends to such a fibration of the entire sphere, a result previously known only in dimension three.
"Germs of fibrations of spheres by great circles always extend to the whole sphere." Algebr. Geom. Topol. 18 (3) 1323 - 1360, 2018. https://doi.org/10.2140/agt.2018.18.1323