论文标题
在史密斯课程中，货车Kampen阻塞和嵌入$ [3]*k $
On the Smith classes, the van Kampen obstruction and embeddability of $[3]*K$
论文作者
论文摘要
在这篇调查研究论文中，我们首先介绍了史密斯阶级的复合体理论，上面有免费的，周期性的地图。这些类定义为简单复合物$ k $的已删除产品，与$ k $的嵌入类相同。反过来，嵌入课程是van kampen障碍班的概括，即嵌入$ d $ d $二维的复合物$ k $ $ k $ in Euclidean $ 2D $ -SPACE。所有这些概念都将简单地引入。其次，我们使用第一部分中介绍的理论将复杂$ [3]*k $的嵌入式类（或特殊的史密斯类）与$ k $的嵌入类联系起来。这里$ [3]*k $是$ k $的连接，并共有三个点。具体来说，我们证明，如果$ m $ th嵌入$ k $的类是非零的，则$（m+2）$ - nd嵌入$ [3]*k $的嵌入类是非零的。我们还证明了该定理对$ [3]*k $的嵌入性的一些后果。
In this survey-research paper, we first introduce the theory of Smith classes of complexes with fixed-point free, periodic maps on them. These classes, when defined for the deleted product of a simplicial complex $K$, are the same as the embedding classes of $K$. Embedding classes, in turn, are generalizations of the van Kampen obstruction class for embeddability of a $d$-dimensional complex $K$ into the Euclidean $2d$-space. All of these concepts will be introduced in simple terms. Second, we use the theory introduced in the first part to relate the embedding classes (or the special Smith classes) of the the complex $[3]*K$ with the embedding classes of $K$. Here $[3]*K$ is the join of $K$ with a set of three points. Specifically, we prove that if the $m$-th embedding class of $K$ is non-zero, then the $(m+2)$-nd embedding class of $[3]*K$ is non-zero. We also prove some of the consequences of this theorem for the embeddability of $[3]*K$.
