Example of Singular Reduction...
November 1, 2014, update March 5, 2015
 
This is an example of symplectic reduction in diffeology where the spaces involved are 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 the symplectic form, restricted to a generic level of the moment map, passes to the reduced space. That is a very informative example of symplectic reduction in presence of singularities.
 Ref: Patrick Iglesias-Zemmour. Example of Singular Reduction in Symplectic Diffeology. Proc. Amer. Math. Soc., Volume 144, Number 3, Pages 1309–1324, USA R.I. March 2016. (Article electronically published on August 12, 2015, http://dx.doi.org/10.1090/proc12772.)http://www.ams.org/publications/journals/journalsframework/prochttp://dx.doi.org/10.1090/proc12772shapeimage_3_link_0shapeimage_3_link_1