Poisson structures whose Poisson diffeomorphism group is not locally path-connected
[Structures de Poisson dont le groupe de difféomorphismes de Poisson n’est pas localement connexe par arcs]
MărcuȚ, Ioan1
1 Radboud University Nijmegen, 6500 GL Nijmegen, (The Netherlands)
Annales Henri Lebesgue, Tome 4 (2021), pp. 1521-1529.

Nous construisons des exemples de structures de Poisson dont le groupe de difféomorphismes de Poisson n’est pas localement connexe par arcs.

We build examples of Poisson structure whose Poisson diffeomorphism group is not locally path-connected.

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DOI : 10.5802/ahl.108
Classification : 53D17, 58D05, 57S05
Mots clés : Poisson manifold, Poisson diffeomorphisms
MărcuȚ, Ioan 1

1 Radboud University Nijmegen, 6500 GL Nijmegen, (The Netherlands) 
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     title = {Poisson structures whose {Poisson} diffeomorphism group is not locally path-connected},
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     publisher = {\'ENS Rennes},
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     year = {2021},
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     language = {en},
     url = {http://www.numdam.org/articles/10.5802/ahl.108/}
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MărcuȚ, Ioan. Poisson structures whose Poisson diffeomorphism group is not locally path-connected. Annales Henri Lebesgue, Tome 4 (2021), pp. 1521-1529. doi : 10.5802/ahl.108. http://www.numdam.org/articles/10.5802/ahl.108/

[Ban98] Banyaga, Augustin On Poisson Diffeomorphisms, Analysis on infinite dimensional Lie groups and algebras (Heyer, H.; Marion, J., eds.), World Scientific, 1998, pp. 1-8 | Zbl

[Ham82] Hamilton, Richard S. The inverse function theorem of Nash and Moser, Bull. Am. Math. Soc., Volume 7 (1982) no. 1, pp. 65-222 | DOI | MR | Zbl

[KM97] Kriegl, Andreas; Michor, Peter W. The Convenient Setting of Global Analysis, Mathematical Surveys and Monographs, 53, American Mathematical Society, 1997 | DOI | Zbl

[Mil84] Milnor, John W. Remarks on infinite-dimensional Lie groups, Relativity, groups and topology, II (Les Houches, 1983), North-Holland, 1984, pp. 1007-1057 | Zbl

[Ryb01] Rybicki, Tomasz On foliated, Poisson and Hamiltonian diffeomorphisms, Diff. Geom. Appl., Volume 15 (2001) no. 1, pp. 33-46 | DOI | MR | Zbl

[SW15] Schmeding, Alexander; Wockel, Christoph The Lie group of bisections of a Lie groupoid, Ann. Global Anal. Geom., Volume 48 (2015) no. 1, pp. 87-123 | DOI | MR | Zbl

[Wei71] Weinstein, Alan Symplectic manifolds and their lagrangian submanifolds, Adv. Math., Volume 6 (1971), pp. 329-346 | DOI | MR | Zbl

[Xu97] Xu, Ping Flux homomorphism on symplectic groupoids, Math. Z., Volume 226 (1997) no. 4, pp. 575-597 | MR | Zbl

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