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2014 Rigidity around Poisson submanifolds
Ioan Mărcuţ
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Acta Math. 213(1): 137-198 (2014). DOI: 10.1007/s11511-014-0118-1

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].

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Ioan Mărcuţ. "Rigidity around Poisson submanifolds." Acta Math. 213 (1) 137 - 198, 2014. https://doi.org/10.1007/s11511-014-0118-1

Information

Received: 10 October 2012; Revised: 25 November 2013; Published: 2014
First available in Project Euclid: 30 January 2017

zbMATH: 1310.53071
MathSciNet: MR3261013
Digital Object Identifier: 10.1007/s11511-014-0118-1

Rights: 2014 © Institut Mittag-Leffler

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Vol.213 • No. 1 • 2014
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