A volume-preserving counterexample to the Seifert conjecture
Dynamical Systems
2009-09-25 v1
Abstract
We prove that every 3-manifold possesses a , 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, 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.
Keywords
Cite
@article{arxiv.math/9504230,
title = {A volume-preserving counterexample to the Seifert conjecture},
author = {Greg Kuperberg},
journal= {arXiv preprint arXiv:math/9504230},
year = {2009}
}