Reference : Futaki invariant for Fedosov star products
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Physical, chemical, mathematical & earth Sciences : Mathematics
Futaki invariant for Fedosov star products
La Fuente-Gravy, Laurent mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
[en] symplectic connections ; moment map ; deformation quantization ; closed star products ; Kähler manifolds
[en] 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

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