Rigidity around Poisson submanifolds

Ioan Mărcuţ Department of Mathematics, University of Illinois at Urbana-Champaign

Mathematical Physics mathscidoc:1701.22003

Acta Mathematica, 213, (1), 137-198, 2012.10
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 compute the Poisson moduli space of the sphere in the dual of a compact semisimple Lie algebra [17].
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@inproceedings{ioan2012rigidity,
  title={Rigidity around Poisson submanifolds},
  author={Ioan Mărcuţ},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203403529130794},
  booktitle={Acta Mathematica},
  volume={213},
  number={1},
  pages={137-198},
  year={2012},
}
Ioan Mărcuţ. Rigidity around Poisson submanifolds. 2012. Vol. 213. In Acta Mathematica. pp.137-198. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203403529130794.
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