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Formal equivalence of
Poisson structures around Poisson submanifolds
Ioan Mărcuţ |
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Vol. 255 (2012), No. 2, 439–461
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Abstract |
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Let (M,π) be a Poisson manifold. A Poisson submanifold P ⊂ M gives rise to a Lie algebroid AP → P. Formal deformations of π around P are controlled by certain cohomology groups associated to AP. Assuming that these groups vanish, we prove that π is formally rigid around P; that is, any other Poisson structure on M, with the same first-order jet along P, is formally Poisson diffeomorphic to π. When P is a symplectic leaf, we find a list of criteria that are sufficient for these cohomological obstructions to vanish. In particular, we obtain a formal version of the normal form theorem for Poisson manifolds around symplectic leaves. |
Keywords
Poisson geometry, Lie algebroid, graded Lie algebra
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Mathematical Subject Classification 2010
Primary: 53D17, 58H15
Secondary: 70K45, 17B55, 17B70
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Milestones
Received: 27 November 2010
Revised: 29 June 2011
Accepted: 7 July 2011
Published: 10 April 2012
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Authors |
| Ioan Mărcuţ | |
| Department of Mathematics Utrecht University 3508 TA Utrecht The Netherlands |
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