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Seifert Conjecture

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 Eric W. Weisstein
1999-05-26