A volume-preserving counterexample to the Seifert conjecture
Open Access Publications from the University of California

## A volume-preserving counterexample to the Seifert conjecture

• Author(s): Kuperberg, Greg
• et al.

## Published Web Location

https://arxiv.org/pdf/math/9504230.pdf
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Abstract

We prove that every 3-manifold possesses a $C^1$, 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, $C^\infty$ 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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