论文标题
关于$ [3]*k $的嵌入性
On the embeddability of $[3]*K$
论文作者
论文摘要
我们将简单复合物$ [3]*k $的嵌入性与$ \ Mathbb {r}^{n+2} $与$ k $的嵌入性与$ \ Mathbb {r}^n $相关联。简而言之，在亚稳态范围内，$ k $的嵌入性在$ \ mathbb {r}^n $中，$ 2N \ geq 3（d+1）$，等同于$ [3]*k $ in $ \ \ \ \ \ \ m athbb {r}^{r}^{n+2} $的嵌入性。此外，只有$ k $ $ k $的货车障碍物消失了，只有当时货车坎皮阻塞$ [3]*k $消失。因此，对于$ d = 2 $，嵌入$ [3]*k $的嵌入与消失的van kampen障碍物的消失相当于$ k $，但没有$ k $的嵌入性。
We relate the embeddability of the simplicial complex $[3]*K$ into $\mathbb{R}^{n+2}$ to that of $K$ into $\mathbb{R}^n$. In brief, the embeddability of $K$ into $\mathbb{R}^n$, in the metastable range $2n\geq 3(d+1)$, is equivalent to the embeddability of $[3]*K$ into $\mathbb{R}^{n+2}$. We show moreover than the van Kampen obstruction of $K$ vanishes if and only if the van Kampen obstruction of $[3]*K$ vanishes. It follows that for $d=2$, embeddabilty of $[3]*K$ is equivalent with the vanishing of the van Kampen obstruction for $K$, but not with the embeddability of $K$.
