Abstract
We investigate the properties of a two-cocycle on the group of symplectic diffeomorphisms of an exact symplectic manifold defined by Ismagilov, Losik, and Michor. We provide both vanishing and nonvanishing results and applications to foliated symplectic bundles and to Hamiltonian actions of finitely generated groups.
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Acknowledgments
We warmly thank Dusa McDuff for explaining to us the proof of Theorem 1.4 and Example 5.6 (4). We thank Dieter Kotschick for drawing our attention to the paper of Ismagilov, Losik, and Michor. And, last but not least, the anonymous referee for helpful remarks improving the final exposition.
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Ś. Gal was partially supported by Polish MNiSW grant N N201 541738 and Swiss NSF Sinergia Grant CRSI22-130435.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Gal, Ś., Kędra, J. A two-cocycle on the group of symplectic diffeomorphisms. Math. Z. 271, 693–706 (2012). https://doi.org/10.1007/s00209-011-0884-9
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DOI: https://doi.org/10.1007/s00209-011-0884-9