Reference : Futaki invariant for Fedosov star products
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/37316
Futaki invariant for Fedosov star products
English
La Fuente-Gravy, Laurent mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
May-2019
Journal of Symplectic Geometry
International Press
17
5
1317-1330
Yes
International
1527-5256
1540-2347
MA
[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
manifold.
Researchers
http://hdl.handle.net/10993/37316

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