Symplectomorphisms of exotic discs
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Peer-reviewed
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Article
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Abstract
We construct a symplectic structure on a disc that admits a compactly supported symplectomorphism which is not smoothly isotopic to the identity. The symplectic structure has an overtwisted concave end; the construction of the symplectomorphism is based on a unitary version of the Milnor--Munkres pairing. En route, we introduce a symplectic analogue of the Gromoll filtration. The Appendix by S. Courte shows that for our symplectic structure the map from compactly supported symplectic mapping classes to compactly supported smooth mapping classes is in fact surjective.
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Journal de l’École polytechnique — Mathématiques
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Journal ISSN
2429-7100
2270-518X
2270-518X
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5
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Cellule MathDoc/CEDRAM
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Engineering and Physical Sciences Research Council (EP/N01815X/1)
R.C. is supported by NSF grant DMS-1608018 and a BBVA Research Fellowship. A.K. was partially supported by NSF grant DMS{1505798, by a Junior Fellow award from the Simons Foundation, and by NSF grant DMS-1128155 whilst at the Institute for Advanced Study. I.S. is partially supported by a Fellowship from the EPSRC.