有理秩的Hasse图
A Hasse diagram for rational toral ranks
摘要：
设$X$是具有有限有理上同调的单连通CW复形.对于由基于有理toral秩的等价关系导出的几乎自由toral作用${\mathcal T}_0(X)=\{[Y_i] \}$得到的$X$的有理化轨道空间的有限商集，如果对某个$n>0$存在有理化Borel纤维化$Y_i\to Y_j\to BT^n_{\Q}$，则我们将其排序为$[Y_i]<[Y_j]$.它表现出对$X$的几乎自由的横向作用。本文讨论偏序集${\mathcal T}_0(X)$的Hasse图${\mathcal H}(X)$，它构成一个基图$G{\mathcal H}(X)$，并给出一些例子.最后我们将尝试把$G{\mathcal H}(X)$看作是以$X_{\Q}$为基点的有限CW复形${\mathcal T}(X)$的1-骨架。
英文摘要：
Let $X$ be a simply connected CW complex with finite rational cohomology. For the finite quotient set of rationalized orbit spaces of $X$ obtained by almost free toral actions, ${\mathcal T}_0(X)=\{[Y_i] \}$, induced by an equivalence relation based on rational toral ranks, we order as $[Y_i]<[Y_j]$ if there is a rationalized Borel fibration $Y_i\to Y_j\to BT^n_{\Q}$ for some $n>0$. It presents a variation of almost free toral actions on $X$. We consider about the Hasse diagram ${\mathcal H}(X)$ of the poset ${\mathcal T}_0(X)$, which makes a based graph $G{\mathcal H}(X)$, with some examples. Finally we will try to regard $G{\mathcal H}(X)$ as the 1-skeleton of a finite CW complex ${\mathcal T}(X)$ with base point $X_{\Q}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
