Poisson structures whose Poisson diffeomorphism group is not locally path-connected
Annales Henri Lebesgue, Volume 4 (2021), pp. 1521-1529.

Metadata

Keywords Poisson manifold, Poisson diffeomorphisms

Abstract

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


References

[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