Article (Scientific journals)
Quantum moment map and obstructions to the existence of closed Fedosov star products
Futaki, Akito; La Fuente-Gravy, Laurent
2021In Journal of Geometry and Physics, 163
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Abstract :
[en] It is shown that the normalized trace of Fedosov star product for quantum moment map depends only on the path component in the cohomology class of the symplectic form and the cohomology class of the closed formal 2-form required to define Fedosov connections (Theorem 1.3). As an application we obtain a family of obstructions to the existence of closed Fedosov star products naturally attached to symplectic manifolds (Theorem 1.5) and Kähler manifolds (Theorem 1.6). These obstructions are integral invariants depending only on the path component of the cohomology class of the symplectic form. Restricted to compact Kähler manifolds we re-discover an obstruction found earlier in La Fuente-Gravy (2019).
Disciplines :
Mathematics
Author, co-author :
Futaki, Akito;  Tsinghua University > Yau Mathematical Science Center > Professor
La Fuente-Gravy, Laurent ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
External co-authors :
yes
Language :
English
Title :
Quantum moment map and obstructions to the existence of closed Fedosov star products
Publication date :
May 2021
Journal title :
Journal of Geometry and Physics
ISSN :
0393-0440
Publisher :
Elsevier, Amsterdam, Netherlands
Volume :
163
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 08 January 2021

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