关于辛流形上星积的示性类的几何
On the geometry of the characteristic class of a star product on a symplectic manifold
摘要：
辛流形上的星积的示性类表现为给定辛联络的变形类，如费多索夫所描述的。相反，人们通常认为星积的示性类是泊松结构的变形类（如Kontsevich的工作）。在本文中，我们提出了，在辛框架下，一个自然的过程，通过直接量化的辛结构的变形构造一个星积。基本上，在Fedosov的零示性类星积的递归公式中，我们用参数$\hbar$中的一个形式变形来代替辛结构。然后，我们证明了每一个等价类的星产品包含这样的元素。此外，在一个给定的类中，这种星积之间的等价性是由形式的单参数的类同态族来实现的，正如莫泽的论证所产生的那样。
英文摘要：
The characteristic class of a star product on a symplectic manifold appears as the class of a deformation of a given symplectic connection, as described by Fedosov. In contrast, one usually thinks of the characteristic class of a star product as the class of a deformation of the Poisson structure (as in Kontsevich's work). In this paper, we present, in the symplectic framework, a natural procedure for constructing a star product by directly quantizing a deformation of the symplectic structure. Basically, in Fedosov's recursive formula for the star product with zero characteristic class, we replace the symplectic structure by one of its formal deformations in the parameter $\hbar$. We then show that every equivalence class of star products contains such an element. Moreover, within a given class, equivalences between such star products are realized by formal one-parameter families of diffeomorphisms, as produced by Moser's argument.
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