Example of singular reduction in symplectic diffeology

Patrick Iglesias-Zemmour (1, 2)

1 HUJ - The Hebrew University of Jerusalem
2 I2M - Institut de Mathématiques de Marseille

We present an example of symplectic reduction in diffeology where the space involved is infinite dimensional and the reduction is singular. This example is a mix of two cases that are not handled by ordinary symplectic geometry. We show that, in this infinite dimensional example, the singularities are distributed in such a way that the symplectic form, restricted to a generic level of the moment map, passes to the reduced space.

Mots clés: symplectic geometry; diffeology

Domaines: Géométrie symplectique [math.SG]

Patrick Iglesias-Zemmour. Example of singular reduction in symplectic diffeology. Proceedings of the American Mathematical Society, 2016, 144 (3), pp.1309-1324. ⟨10.1090/proc12772⟩. ⟨hal-01288677⟩