A volume-preserving counterexample to the Seifert conjecture
- Cite this article as:
- Kuperberg, G. Commentarii Mathematici Helvetici (1996) 71: 70. doi:10.1007/BF02566410
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We prove that every 3-manifold possesses aC1, volume-preserving flow with no fixed points and no closed trajectories. The main construction is a volume-preserving version of the Schweitzer plug. We also prove that every 3-manifold possesses a volume-preserving,C∞ flow with discrete closed trajectories and no fixed points (as well as a PL flow with the same geometry), which is needed for the first result. The proof uses a Dehn-twisted Wilson-type plug which also preserves volume.