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Free circle actions with contractible orbits on symplectic manifolds

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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 the constructions of FGM.

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  1. Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstr. 39, 80333, München, Germany

    D. Kotschick

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  1. D. Kotschick
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Correspondence to D. Kotschick.

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Kotschick, D. Free circle actions with contractible orbits on symplectic manifolds. Math. Z. 252, 19–25 (2006). https://doi.org/10.1007/s00209-005-0841-6

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  • DOI: https://doi.org/10.1007/s00209-005-0841-6

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