Article (Scientific journals)
Futaki invariant for Fedosov star products
La Fuente-Gravy, Laurent
2019In Journal of Symplectic Geometry, 17 (5), p. 1317-1330
Peer reviewed
 

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Keywords :
symplectic connections; moment map; deformation quantization; closed star products; Kähler manifolds
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
La Fuente-Gravy, Laurent ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
Futaki invariant for Fedosov star products
Publication date :
May 2019
Journal title :
Journal of Symplectic Geometry
ISSN :
1540-2347
Publisher :
International Press, United States - Massachusetts
Volume :
17
Issue :
5
Pages :
1317-1330
Peer reviewed :
Peer reviewed
Available on ORBilu :
since 16 November 2018

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