Poisson Structures and Their Normal Forms

By J. Dufour, T. Nguyen. 2005

303 citations recorded by the source corpus.

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Citations in the corpus

Splitting theorems for Poisson and related structures (2016, background): “ν(M,N). Then the lower horizontal map becomes Tp, and the left vertical map an anchor map for ν(E,i!E). But the ﬁber product of Tν(M,N) and i!Eover TN is exactly p!i!E, by deﬁnition. We conclude that (18) ν(E,i!E) → i!E×TνN, ξ→ pi!E(ξ), ν(a)(ξ) deﬁnes an injective morphism of double vector bundles ν”
On the linearization theorem for proper Lie groupoids (2011, background): “andard hypothesis are that Lis compact and the holonomy at xis ﬁnite; i.e. precisely the s-properness of G at x. Example 1.16. A similar discussion applies when G is the symplectic groupoid (see e.g. [7]) associated to a Poisson manifold (M,π). The resulting linearizability problems are closely rela”
Lectures on integrability of Lie brackets (2006, background): “ the book by Cannas da Silva and Weinstein [7] devoted to the geometry of noncommutative objects, the book by Moerdijk and Mrˇcun [44] on Lie groupoids and foliations, and the book by Dufour and Zung [20] on Poisson geometry. Several important aspects of Lie groupoid theory have not made it yet to e”
Lie groupoids and their orbispaces (2012, unknown): “The ﬁrst proof of Zung’s Theorem appeared in [28], see also [11].”
Multiplicative forms and Spencer operators (2012, background): “[17]), which is assumed to come from an s-simply connected Lie groupoid Σ.”
PROPER GROUPOIDS AND MOMENTUM MAPS: LINEARIZATION, AFFINITY, AND CONVEXITY GROUPOPROPRES ET APPLICATIONS MOMENT: LIN ´ EARISATION, CARACT ` ERE AFFINE, ET CONVEXIT ´ E (2004, methodology): “ to a tubular neighborhood of the zero section in NO (and also isomorphic to GO ⋉NO itself). We will now apply Theorem 2.3 to the case of symplectic and quasi-symplectic groupoids. Recall (see, e.g., [5, 7]) that a symplectic groupoid is a Lie groupoid Γ ⇒P, where Γ is equipped with a symplectic for”
Poisson (co)homology and isolated singularities (2005, methodology): “We recall that the Poisson complex is constructed in the following way (see [4] and [11] for details).”