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.

© 1996-9

1999-05-26