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Example of singular reduction in symplectic diffeology


Author: Patrick Iglesias-Zemmour
Journal: Proc. Amer. Math. Soc. 144 (2016), 1309-1324
MSC (2010): Primary 53Dxx, 58Axx; Secondary 53D20, 53D99, 58A99
Published electronically: August 12, 2015
MathSciNet review: 3025051
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Abstract: 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.


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Additional Information

Patrick Iglesias-Zemmour
Affiliation: UMR-7373 CNRS France – and – Department of Mathematics, Hebrew University of Jerusalem, Givat-Ram Campus, 91904 Jerusalem, Israel
Email: piz@math.huji.ac.il

DOI: https://doi.org/10.1090/proc12772
Received by editor(s): November 2, 2014
Received by editor(s) in revised form: February 19, 2015, and March 4, 2015
Published electronically: August 12, 2015
Communicated by: Michael Wolf
Article copyright: © Copyright 2015 American Mathematical Society