Poisson geometry around Poisson submanifolds

  • Rui Loja Fernandes

    University of Illinois at Urbana-Champaign, Urbana, USA
  • Ioan Mărcuţ

    Radboud University Nijmegen, Nijmegen, The Netherlands
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Abstract

We construct a first-order local model for Poisson manifolds around a large class of Poisson submanifolds and give conditions under which this model is a local normal form. The resulting linearization theorem includes as special cases all the known linearization theorems for fixed points and symplectic leaves. The symplectic groupoid version of these results gives a solution to the groupoid coisotropic embedding problem.

Cite this article

Rui Loja Fernandes, Ioan Mărcuţ, Poisson geometry around Poisson submanifolds. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1494