Free circle actions with contractible orbits on symplectic manifolds
Symplectic Geometry
2007-05-23 v3 Geometric Topology
Abstract
We prove that closed symplectic four-manifolds do not admit any smooth free circle actions with contractible orbits, without assuming that the actions preserve the symplectic forms. In higher dimensions such actions by symplectomorphisms do exist, and we give explicit examples based on a construction of Fernandez, Gray and Morgan. We also prove that the only compact complex surfaces admitting free circle actions with contractible orbits are primary Hopf surfaces.
Keywords
Cite
@article{arxiv.math/0410243,
title = {Free circle actions with contractible orbits on symplectic manifolds},
author = {D. Kotschick},
journal= {arXiv preprint arXiv:math/0410243},
year = {2007}
}
Comments
proof of Prop. 1 clarified, to appear in Mathematische Zeitschrift