Rigidity around Poisson submanifolds
Year: 2014
Type: article
Abstract: 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].
Source: Acta Mathematica
Author: Ioan Mărcuţ
Institution: University of Illinois Urbana-Champaign
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W1962579192