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See detailFutaki invariant for Fedosov star products
La Fuente-Gravy, Laurent UL

in Journal of Symplectic Geometry (2019), 17(5), 1317-1330

We study obstructions to the existence of closed Fedosov star products on a given Kähler manifold (M, omega, J). In our previous paper [11], we proved that if the Levi-Civita connection of a Kähler ... [more ▼]

We study obstructions to the existence of closed Fedosov star products on a given Kähler manifold (M, omega, J). In our previous paper [11], we proved that if the Levi-Civita connection of a Kähler manifold will produce a closed (in the sense of Connes-Flato-Sternheimer [4]) Fedosov’s star product then it is a zero of a moment map μ on the space of symplectic connections. By analogy with the Futaki invariant obstructing the existence of cscK metrics, we build an obstruction for the existence of zero of μ and hence for the existence of closed Fedosov’s star product on a Kähler manifold. [less ▲]

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See detailEquivalences of coisotropic submanifolds
Schatz, Florian UL; Zambon, Marco

in Journal of Symplectic Geometry (2017), 15(1), 107-149

We study the role that Hamiltonian and symplectic diffeomorphisms play in the deformation problem of coisotropic submanifolds. We prove that the action by Hamiltonian diffeomorphisms corresponds to the ... [more ▼]

We study the role that Hamiltonian and symplectic diffeomorphisms play in the deformation problem of coisotropic submanifolds. We prove that the action by Hamiltonian diffeomorphisms corresponds to the gauge-action of the L-infinity-algebra of Oh and Park. Moreover we introduce the notion of extended gauge-equivalence and show that in the case of Oh and Park's L-infinity-algebra one recovers the action of symplectic isotopies on coisotropic submanifolds. Finally, we consider the transversally integrable case in detail. [less ▲]

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