论文标题
循环订购直接产品和障碍物的左订购性
Circularly ordering direct products and the obstruction to left-orderability
论文作者
论文摘要
最近的结果是，$ g $的左订购性与直接产品的循环排序性密切相关。由于主要定理的结果，我们为理性同源性3-Sphere的基本组提供了一个新的特征，可以左右。我们的结果暗示，对于绘制曾经是函数表面的班级组和其他在$ s^1 $的行动的组在同步方面是刚性的，它们的产品$ g \ times \ times \ times \ mathbb {z}/n \ mathbb {z} $是循环订购的。我们还总体上处理了直接产品的循环排序性，处理了承认双重不变循环排序的因素组的案例，以及迭代的直接产品，其因子组可正常。
Motivated by the recent result that left-orderability of a group $G$ is intimately connected to circular orderability of direct products $G \times \mathbb{Z}/n\mathbb{Z}$, we provide necessary and sufficient cohomological conditions that such a direct product be circularly orderable. As a consequence of the main theorem, we arrive at a new characterization for the fundamental group of a rational homology 3-sphere to be left-orderable. Our results imply that for mapping class groups of once-punctured surfaces, and other groups whose actions on $S^1$ are cohomologically rigid, the products $G \times \mathbb{Z}/n\mathbb{Z}$ are seldom circularly orderable. We also address circular orderability of direct products in general, dealing with the cases of factor groups admitting a bi-invariant circular ordering, and iterated direct products whose factor groups are amenable.
