Open AccessExample of singular reduction in symplectic diffeology
Author(s) -
Patrick Iglesias-Zemmour
Publication year - 2015
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc12772
Subject(s) - symplectic geometry , moment map , reduction (mathematics) , mathematics , symplectomorphism , gravitational singularity , symplectic matrix , space (punctuation) , pure mathematics , symplectic representation , symplectic vector space , moment (physics) , mathematical analysis , geometry , computer science , physics , classical mechanics , operating system
International audienceWe 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