论文标题
泊松还原的强质量结构
The Strong Homotopy Structure of Poisson Reduction
论文作者
论文摘要
在本文中，我们建议根据$ l_ \ infty $ grphimiss对多人字段的简化方案。使用还原流的歧管的众所周知的几何特性，我们执行了泰勒的泰勒膨胀，这使我们能够建立合适的DGLA的变形缩回。我们首先获得了$ l_ \ infty $ - 预测和通用DGLA缩回的 - 包含的明确公式。然后，我们将此公式应用于我们在减少歧管上的多生物场中构建的变形缩回。这使我们能够获得所需的减少$ l_ \ infty $ - morphermism。最后，我们与其他还原程序进行了比较。
In this paper we propose a reduction scheme for multivector fields phrased in terms of $L_\infty$-morphisms. Using well-know geometric properties of the reduced manifolds we perform a Taylor expansion of multivector fields, which allows us to built up a suitable deformation retract of DGLA's. We first obtained an explicit formula for the $L_\infty$-Projection and -Inclusion of generic DGLA retracts. We then applied this formula to the deformation retract that we constructed in the case of multivector fields on reduced manifolds. This allows us to obtain the desired reduction $L_\infty$-morphism. Finally, we perfom a comparison with other reduction procedures.
