双变余各向同性上的星表示
Star-Representations sur des sous-varietes co-isotropes
摘要：
对于Poisson流形X的共各向同性（或第一类）子流形C，我们考虑星积，使得C的消失理想I成为变形代数中的左理想，从而在C上的光滑函数空间上定义了左模结构。我们展示了如何可以推导出一个正式的猜想一个拉Tamarkin推广到上链与C兼容。为此，我们首先证明了相容多向量域空间与相容多微分算子之间的一个Hochschild-Kostant-Rosenberg定理。然后，我们给后者赋予了一个G-无穷结构，并证明了形式的障碍是由某些上同调群控制的，当C是向量空间M的一个子向量空间时，我们约化了这些上同调群.在余维1中，我们猜想--受到低维例子和Gloessner表示定理（1998）的鼓励--形式成立。对于更高的余维，这不是不可能的障碍物发生，在辛的情况下，是链接到Atiyah-Molino类的一个定期叶理。
英文摘要：
For a coisotropic (or first-class) submanifold C of a Poisson manifold X we consider star-products for which the vanishing ideal I of C becomes a left ideal in the deformed algebra thus defining a left module structure on the space of smooth functions on C. We show how this can be deduced from a formality conjecture a la Tamarkin generalized to cochains compatible with C. To this end we first prove a theorem a la Hochschild-Kostant-Rosenberg between the space of compatible multivector fields and compatible multidifferential operators. We then equip the latter with a G-infinity structure, and prove that the obstructions to the formality are controlled by certain cohomology groups which we reduce in the case of C being a subvectorspace of the vectorspace M. In codimension 1 we conjecture -encouraged by low-dimensional examples and Gloessner's representation theorem (1998)- that formality holds. For higher codimensions it is not impossible that obstructions occur which in the symplectic case are linked to the Atiyah-Molino class of a regular foliation.
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