论文标题
部分可观测时空混沌系统的无模型预测
Equivariant Bordism of 2-Torus Manifolds and Unitary Toric Manifolds
论文作者
论文摘要
与群体作用的多种流形分类是转化组研究中的重要主题。我们在2-torus group $ \ mathbb {z} _2^n $和torus group $ t^n $的动作中很有趣，并研究了2-torus歧管和单一折叠式歧管的e夫尔式bordism。在本文中，我们给出了$ \ Mathcal {z} _n（\ Mathbb {z} _2^n）$ 2-torus歧管的新描述，并确定$ \ Mathcal {z} _n（\ Mathbb {Z} _2^n）$ as $ as a $ \ bb}的$ \ Mathcal {Z} _n（Z} _n（Z} _n（Z} _n）借助复曲面拓扑，吕和谭证明了bordism $ \ mathcal {z} _n（\ mathbb {z} _2^n）$是由小型封面生成的。我们将为这个结果提供新的证明。这些结果可以推广到统一折叠的层次歧管的等效界，也就是说，我们将对单位折线的组$ \ Mathcal {z} _n^u（t^n）$进行新的描述，并证明$ \ \ \ \ \ \ nathcal {z} _n^u（t^n）$可以由quasnicivations生成。
The equivariant bordism classification of manifolds with group actions is an essential subject in the study of transformation groups. We are interesting in the action of 2-torus group $\mathbb{Z}_2^n$ and torus group $T^n$, and study the equivariant bordism of 2-torus manifolds and unitary toric manifolds. In this paper, we give a new description of the group $\mathcal{Z}_n(\mathbb{Z}_2^n)$ of 2-torus manifolds, and determine the dimention of $\mathcal{Z}_n(\mathbb{Z}_2^n)$ as a $\mathbb{Z}_2$-vector space. With the help of toric topology, Lü and Tan proved that the bordism groups $\mathcal{Z}_n(\mathbb{Z}_2^n)$ are generated by small covers. We will give a new proof to this result. These results can be generalized to the equivariant bordism of unitary toric manifolds, that is, we will give a new description of the group $\mathcal{Z}_n^U(T^n)$ of unitary torus manifolds, and prove that $\mathcal{Z}_n^U(T^n)$ can be generated by quasitoric manifolds with omniorientations.
