论文标题
关于联接的嵌入性及其“因素”
On embeddability of joins and their `factors'
论文作者
论文摘要
我们提供了一个简短而清晰的证明，证明了Melikhov-Schepin 2006年结果的以下特定情况：让$ k $为$ k $二维的简单综合体和$ k*[3] $沿其共同基础，超过$ k $的三个锥体的结合。如果$ 2D \ ge3k+3 $和$ k*[3] $嵌入到$ \ mathbb r^{d+2} $中，则$ k $嵌入到$ \ mathbb r^d $中。 我们还提出了该定理的概括。这些证明基于Haefliger-weber“配置空间”的嵌入性标准，等效性悬架定理以及连接和锥的简单属性。
We present a short and clear proof of the following particular case of a 2006 result of Melikhov-Schepin: Let $K$ be a $k$-dimensional simplicial complex and $K*[3]$ the union of three cones over $K$ along their common bases. If $2d\ge3k+3$ and $K*[3]$ embeds into $\mathbb R^{d+2}$, then $K$ embeds into $\mathbb R^d$. We also present a generalization of this theorem. The proofs are based on the Haefliger-Weber `configuration spaces' embeddability criterion, equivariant suspension theorem and simple properties of joins and cones.
