论文标题
部分可观测时空混沌系统的无模型预测
Embeddability of joins and products of polyhedra
论文作者
论文摘要
我们提供了S. Parsa定理的简短证明，表明存在紧凑的$ n $ -polyhedron $ p $，$ n \ ge 2 $，在$ \ Mathbb r^{2n} $中不可用，因此$ p*p*p*p $ embed in $ \ mathbb r^r^{4n nn+2} $。该证明可以用作使用几何共同体的展示。 我们还表明，$ \ mathbb r^m $，$ m \ ge \ frac {3（n+1）} 2 $ complact $ n $ -polyhedron $ x $ embed in $ \ mathbb r^m $ - $ x*k $嵌入$ \ mathbb r^{m+2k} $，其中$ k $是$（k-1）$ - $ 2K $ -SIMPLEX的骨架;或者 - $ x*l $嵌入$ \ mathbb r^{m+2k} $，其中$ l $是$ 3 $ - 点集的$ k $副本的JOIN;或者 - $ x $是acyclic，$ x \ times \ text {（triod）}^k $嵌入$ \ mathbb r^{m+2k} $。
We present a short proof of S. Parsa's theorem that there exists a compact $n$-polyhedron $P$, $n\ge 2$, non-embeddable in $\mathbb R^{2n}$, such that $P*P$ embeds in $\mathbb R^{4n+2}$. This proof can serve as a showcase for the use of geometric cohomology. We also show that a compact $n$-polyhedron $X$ embeds in $\mathbb R^m$, $m\ge\frac{3(n+1)}2$, if either - $X*K$ embeds in $\mathbb R^{m+2k}$, where $K$ is the $(k-1)$-skeleton of the $2k$-simplex; or - $X*L$ embeds in $\mathbb R^{m+2k}$, where $L$ is the join of $k$ copies of the $3$-point set; or - $X$ is acyclic and $X\times\text{(triod)}^k$ embeds in $\mathbb R^{m+2k}$.
