关于透镜空间的消去正方形
On the deleted squares of lens spaces
摘要：
流形$M$中不同点的序偶的位形空间$F_2 (M)$，也被称为$M$的删除正方形，不是$M$的同伦不变量：Longoni和Salvatore给出了同伦等价的三维透镜空间$M$和$N$的例子，其中$F_2 (M)$和$F_2 (N)$不是同伦等价的。本文研究了两个任意$3$维透镜空间$M$和$N$是否同胚以使$F_2 (M)$和$F_2 (N)$同伦等价的自然问题.我们的工具包括删除正方形的Cheeger-Simons微分特征及其通用覆盖的Massey产品。
英文摘要：
The configuration space $F_2 (M)$ of ordered pairs of distinct points in a manifold $M$, also known as the deleted square of $M$, is not a homotopy invariant of $M$: Longoni and Salvatore produced examples of homotopy equivalent lens spaces $M$ and $N$ of dimension three for which $F_2 (M)$ and $F_2 (N)$ are not homotopy equivalent. In this paper, we study the natural question whether two arbitrary $3$-dimensional lens spaces $M$ and $N$ must be homeomorphic in order for $F_2 (M)$ and $F_2 (N)$ to be homotopy equivalent. Among our tools are the Cheeger--Simons differential characters of deleted squares and the Massey products of their universal covers.
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