论文标题
奇异叶的模块化类
The modular class of a singular foliation
论文作者
论文摘要
规则叶片的模块化类是对叶子矢量场下方不变的体积形式的存在的共同体障碍。通过利用谎言代数和常规叶子之间的关系，本文将模块化类别的概念扩展到了奇异叶子的领域。奇异性是通过用任何通用的谎言$ \ infty $ -Algebroids代替奇异叶来处理的，并通过捡起后者的模块化类别。奇异叶片$ \ nathcal {f} $的模块化类别的几何含义不如常规叶子透明：这是对存在通用谎言$ \ infty $ \ infty $ -AlgeBroid的障碍，$ \ natercal {f} $ berezinian Line bundle bundle bunde $ \ naul trivial $ \ n Mathcal} $ {f}本文说明了使用通用谎言$ \ infty $ -Algebroids将数学概念从常规叶子扩展到奇异的概念的相关性，从而将道路铺平到以这种方式定义其他特征类别的道路。
The modular class of a regular foliation is a cohomological obstruction to the existence of a volume form transverse to the leaves which is invariant under the flow of the vector fields of the foliation. By drawing on the relationship between Lie algebroids and regular foliations, this paper extends the notion of modular class to the realm of singular foliations. The singularities are dealt with by replacing the singular foliations by any of their universal Lie $\infty$-algebroids, and by picking up the modular class of the latter. The geometric meaning of the modular class of a singular foliation $\mathcal{F}$ is not as transparent as for regular foliations: it is an obstruction to the existence of a universal Lie $\infty$-algebroid of $\mathcal{F}$ whose Berezinian line bundle is a trivial $\mathcal{F}$-module. This paper illustrates the relevance of using universal Lie $\infty$-algebroids to extend mathematical notions from regular foliations to singular ones, thus paving the road to defining other characteristic classes in this way.
