共各向同性截面的模与BFV-复形
Moduli of coisotropic sections and the BFV-complex
摘要：
研究Poisson流形中余迷向子流形的局部变形问题。为此，介绍了上各向同性截面广群（关于某些管状邻域）。虽然这个广群的几何内容是显而易见的，但它通常是一个非常复杂的对象。我们提供了一个描述的广群的共各向同性部分的微分分次泊松代数，称为BFV-复杂。这种描述是通过从BFV-复形构造一个广群和从这个广群到上迷向截面广群的满射来实现的。这个态射的核可以很容易地刻画。作为推论，我们得到了BFV-复形的共各向同性截面的模空间与几何Maurer-Cartan元的模空间之间的同构.
英文摘要：
We consider the local deformation problem of coisotropic submanifolds inside Poisson manifolds. To this end the groupoid of coisotropic sections (with respect to some tubular neighbourhood) is introduced. Although the geometric content of this groupoid is evident, it is usually a very intricate object. We provide a description of the groupoid of coisotropic sections in terms of a differential graded Poisson algebra, called the BFV-complex. This description is achived by constructing a groupoid from the BFV-complex and a surjective morphism from this groupoid to the groupoid of coisotropic sections. The kernel of this morphism can be easily chracterized. As a corollary we obtain an isomorphism between the moduli space of coisotropic sections and the moduli space of geometric Maurer-Cartan elements of the BFV-complex.
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