Existence of 'Darboux chart' on loop space
Differential Geometry
2013-11-18 v2 Symplectic Geometry
Abstract
For a finite dimensional symplectic manifold with a symplectic form , corresponding loop space () admits a weak symplectic form . We prove that the loop space over admits Darboux chart for the weak symplectic structure . Further, we show that inclusion map from the symplectic cohomology (as defined by Kriegl and Michor \cite{KM}) of the loop space over to the De Rham cohomology of the loop space is an isomorphism.
Cite
@article{arxiv.1309.2190,
title = {Existence of 'Darboux chart' on loop space},
author = {Pradip Kumar},
journal= {arXiv preprint arXiv:1309.2190},
year = {2013}
}
Comments
9 pages[Updated]