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arXiv · 1612.02946

Futaki invariant for Fedosov's star products

Laurent La Fuente-Gravy
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Abstract

We study obstructions to the existence of closed Fedosov's star products on a given Kähler manifold. In our previous paper, we proved that the Levi-Civita connection of a Kähler manifold will produce a closed (in the sense of Connes-Flato-Sternheimer) Fedosov's star product only if it is a zero of the Cahen-Gutt moment map 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 the moment map and hence for the existence of closed Fedosov's star products on a Kähler manifold.

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Laurent La Fuente-Gravy. 2016-12-09. Futaki invariant for Fedosov's star products. https://arxiv.org/abs/1612.02946

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