|
|
|
Every smooth Nonzero Vector Field on the 3-Sphere has at least one closed orbit. The conjecture was proposed in 1950, proved true for Hopf fibrations, but proved false in general by Kuperberg (1994).
References
Kuperberg, G. ``A Volume-Preserving Counterexample to the Seifert Conjecture.'' Comment. Math. Helv. 71, 70-97, 1996.
Kuperberg, G. and Kuperberg, K. ``Generalized counterexamples to the Seifert Conjecture.'' Ann. Math. 143, 547-576, 1996.
Kuperberg, G. and Kuperberg, K. ``Generalized Counterexamples to the Seifert Conjecture.'' Ann. Math. 144, 239-268, 1996.
Kuperberg, K. ``A Smooth Counterexample to the Seifert Conjecture.'' Ann. Math. 140, 723-732, 1994.