Acta Mathematica

Rigidity around Poisson submanifolds

Ioan Mărcuţ

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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].

Article information

Source
Acta Math., Volume 213, Number 1 (2014), 137-198.

Dates
Received: 10 October 2012
Revised: 25 November 2013
First available in Project Euclid: 30 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485801838

Digital Object Identifier
doi:10.1007/s11511-014-0118-1

Mathematical Reviews number (MathSciNet)
MR3261013

Zentralblatt MATH identifier
1310.53071

Rights
2014 © Institut Mittag-Leffler

Citation

Mărcuţ, Ioan. Rigidity around Poisson submanifolds. Acta Math. 213 (2014), no. 1, 137--198. doi:10.1007/s11511-014-0118-1. https://projecteuclid.org/euclid.acta/1485801838


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