Abstract
Informally, the Darboux–Weinstein theorem says that given any two symplectic manifolds of the same finite dimension, they look alike locally. It states that around any point of a symplectic manifold, there is a chart for which the symplectic form has a particularly nice form. In this section, we give a proof of an equivariant version of the theorem and look at some corollaries. We direct the reader to [1] or Sect. 22 of [2] for more details.
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References
M. Audin, Torus Actions on Symplectic Manifolds, vol. 93, Progress in Mathematics (Birkhäuser, Birkhäuser, 2004)
V. Guillemin, S. Sternberg, Symplectic Techniques in Physics (Cambridge University Press, Cambridge, 1986)
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Dwivedi, S., Herman, J., Jeffrey, L.C., van den Hurk, T. (2019). The Darboux–Weinstein Theorem. In: Hamiltonian Group Actions and Equivariant Cohomology. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-27227-2_3
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DOI: https://doi.org/10.1007/978-3-030-27227-2_3
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