论文标题
D-明显作为嵌入问题
d-representability as an embedding problem
论文作者
论文摘要
如果记录了$ \ mathbb {r}^d $中的凸集集合的相交模式，则据说一个抽象的简单综合体可说是$ d $的。在本文中，我们表明，简单复合物的$ d $表述相当于具有某些属性的地图的存在，从密切相关的简单复合物到$ \ mathbb {r}^d $。这种等价表明，使用拓扑方法（例如Borsuk-Ulam定理的申请）证明（和证明）$ d $的$ D $证明，我们开始探索。
An abstract simplicial complex is said to be $d$-representable if it records the intersection pattern of a collection of convex sets in $\mathbb{R}^d$. In this paper, we show that $d$-representability of a simplicial complex is equivalent to the existence of a map with certain properties, from a closely related simplicial complex into $\mathbb{R}^d$. This equivalence suggests a framework for proving (and disproving) $d$-representability of simplicial complexes using topological methods such as applications of the Borsuk-Ulam theorem, which we begin to explore.
