Rigidity around Poisson submanifolds

  title={Rigidity around Poisson submanifolds},
  author={I. Marcut},
  journal={Acta Mathematica},
  • I. Marcut
  • Published 2014
  • Mathematics
  • Acta Mathematica
We prove a rigidity theorem in Poisson geometry around compact Poisson submanifolds, using the Nash–Moser fast convergence method. In the case of one-point submanifolds (fixed points), this implies a stronger version of Conn’s linearization theorem [2], also proving that Conn’s theorem is a manifestation of a rigidity phenomenon; similarly, in the case of arbitrary symplectic leaves, it gives a stronger version of the local normal form theorem [7]. We can also use the rigidity theorem to… Expand
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