Commentarii Mathematici Helvetici

, Volume 71, Issue 1, pp 70–97

A volume-preserving counterexample to the Seifert conjecture

  • Greg Kuperberg

DOI: 10.1007/BF02566410

Cite this article as:
Kuperberg, G. Commentarii Mathematici Helvetici (1996) 71: 70. doi:10.1007/BF02566410


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.

Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • Greg Kuperberg
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA