English

Existence of 'Darboux chart' on loop space

Differential Geometry 2013-11-18 v2 Symplectic Geometry

Abstract

For a finite dimensional symplectic manifold (M,ω)(M,\omega) with a symplectic form ω\omega, corresponding loop space (LM=C(S1,M)LM=C^\infty(S^1,M)) admits a weak symplectic form Ωω\Omega^\omega. We prove that the loop space over \mbrn\mbr^n admits Darboux chart for the weak symplectic structure Ωω\Omega^\omega. Further, we show that inclusion map from the symplectic cohomology (as defined by Kriegl and Michor \cite{KM}) of the loop space over Rn\mathbb R^n to the De Rham cohomology of the loop space is an isomorphism.

Keywords

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]

R2 v1 2026-06-22T01:23:27.844Z