Symplectomorphisms of exotic discs
[Symplectomorphismes de disques exotiques]
Journal de l’École polytechnique — Mathématiques, Tome 5 (2018) , pp. 289-316.

Le but principal de cet article est la construction d’une structure symplectique sur un disque avec un symplectomorphisme à support compact qui n’est pas isotope à l’identité. Cette structure symplectique a un bord concave donné par la symplectification d’une structure de contact vrillée. La construction du symplectomorphisme est basée sur une version unitaire de l’accouplement de Milnor-Munkres. En chemin, nous introduisons un analogue symplectique de la filtration de Gromoll. Dans l’appendice, S. Courte montre que, pour notre structure symplectique, l’application qui associe à une classe d’applications symplectiques à support compact une classe d’applications lisses à support compact est surjective.

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.

Reçu le : 2017-04-11
Accepté le : 2018-03-20
Publié le : 2018-04-05
DOI : https://doi.org/10.5802/jep.71
Classification : 57R17,  53D10,  53D15
Mots clés : Symplectomorphisme, structure de contact vrillée, accouplement de Milnor-Munkres, filtration de Gromoll
@article{JEP_2018__5__289_0,
     author = {Roger Casals and Ailsa Keating and Ivan Smith and Sylvain Courte},
     title = {Symplectomorphisms of exotic discs},
     journal = {Journal de l'\'Ecole polytechnique --- Math\'ematiques},
     pages = {289--316},
     publisher = {\'Ecole polytechnique},
     volume = {5},
     year = {2018},
     doi = {10.5802/jep.71},
     zbl = {06988581},
     mrnumber = {3795444},
     language = {en},
     url = {jep.centre-mersenne.org/item/JEP_2018__5__289_0/}
}
Casals, Roger; Keating, Ailsa; Smith, Ivan; Courte, Sylvain. Symplectomorphisms of exotic discs. Journal de l’École polytechnique — Mathématiques, Tome 5 (2018) , pp. 289-316. doi : 10.5802/jep.71. https://jep.centre-mersenne.org/item/JEP_2018__5__289_0/

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