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A volume-preserving counterexample to the Seifert conjecture

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Commentarii Mathematici Helvetici

Abstract

We prove that every 3-manifold possesses aC 1, 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.

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Authors and Affiliations

  1. Department of Mathematics, Yale University, 60637, New Haven, CT, USA

    Greg Kuperberg

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  1. Greg Kuperberg
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Additional information

The author was supported by an NSF Postdoctoral Fellowship, grant #DMS-9107908.

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Kuperberg, G. A volume-preserving counterexample to the Seifert conjecture. Commentarii Mathematici Helvetici 71, 70–97 (1996). https://doi.org/10.1007/BF02566410

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  • DOI: https://doi.org/10.1007/BF02566410

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