Symplectic dynamics and the 3-sphere
Symplectic Geometry
2026-02-10 v2 Geometric Topology
Abstract
Given a knot in a closed connected orientable 3-manifold we prove that if the exterior of the knot admits an aperiodic contact form that is Euclidean near the boundary, then the 3-manifold is diffeomorphic to the 3-sphere and the knot is the unknot.
Keywords
Cite
@article{arxiv.1806.08603,
title = {Symplectic dynamics and the 3-sphere},
author = {Marc Kegel and Jay Schneider and Kai Zehmisch},
journal= {arXiv preprint arXiv:1806.08603},
year = {2026}
}
Comments
version to appear in Israel J. Math