Free circle actions with contractible orbits on symplectic manifolds

Details Free circle actions with contractible orbits on symplectic manifolds Free circle actions with contractible orbits on symplectic manifolds

2004-10-09

arxiv.org/abs/math/0410243v3

Math. Zeitschrift 252 (2006), 19--25

Mathematics

Symplectic Geometry

proof of Prop. 1 clarified, to appear in Mathematische Zeitschrift

Scientific paper

10.1007/s00209-005-0841-6

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.

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