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As it is explained in the comment by Bertram Arnold, Fedosov's quantization works for symplectic manifolds only (and can actually be generalized to regular Poisson manifolds) while Kontsevich's quantization … In the symplectic case, the local deformation quantization is known to exist, and is essentially unique (it's the Moyal-Weyl star-product). …

Welcome to mathoverflow! There is actually a whole paper (in French) about choices of signs for Kontsevich formality: https://arxiv.org/pdf/math/0003003.pdf For instance, they define the Hochschild …

yes, the formula for the weights is the same in whatever setting (differentiable, holomorphic and algebro-geometric). weights are involved in a local formula for a start-product. Indeed, $B_\Gamma$ …

Let $A_0$ be a Poisson algebra and $A$ a deformation quantization of $A_0$ (assume we are in a context when it exists). … Assume you have a quantization map $Q:A_0\to A$, by which I mean a section of the classical limit map $A\to A/(\hbar)=A_0$. …

Point 4. concerning the symplectic case, the main reason why the classification map doesn't depend on any choice is because the quantization is unique. …

A $G_\infty$-morphism $\phi$ is determined by structure maps $\phi^{k_1,\dots,k_n}$, $n\geq1$, $k_1,\dots,k_n\geq1$. The $L_\infty$-part of $\phi$ is the $L_\infty$-morphism $\ell$ with structure ma …

Joseph Donin and Andrei Mudrov have worked a lot on this question... the quantization of conjugacy classes seems to be related to dynamical r-matrices and and the so-called reflection equation. …

The only way I know to construct a formality quasi-morphism for poy-vector fields out of an homotopy is via Tamarkins approach (i.e. $G_\infty$-formality). What Tamrakin does is prove that there is …

One has to choose an identification of a tubular neighborhood $U$ of $L$ in $M$ with a tubular neighborhood $V$ of the zero section of the normal bundle $NL$. Once one has done this, it means that w …