论文标题
与固有链接定理的一些“对话”
Some `converses' to intrinsic linking theorems
论文作者
论文摘要
我们主要结果的一个低维版本是Conway-Gordon-Sachs sachs sachs shorem in Graph $ k_6 $ in 3空间中的以下“匡威”定理： 对于任何整数$ z $，有6点$ 1,2,3,4,5,6 $ 3空间，其中每两个$ i，j $由多边形线$ IJ $连接在一起，一个多边形线的内部与任何其他多边形线路是不连接的，除其他多边形线，除了$偶的3 cyer $ $ $ $ $ \ cybone $ $ cy的内部，对于特殊对$ \ {123,456 \} $是$ 2Z+1 $。 我们证明了一个高维的类似物，这是Segal-Spieê的引理的“匡威”。
A low-dimensional version of our main result is the following `converse' of the Conway-Gordon-Sachs Theorem on intrinsic linking of the graph $K_6$ in 3-space: For any integer $z$ there are 6 points $1,2,3,4,5,6$ in 3-space, of which every two $i,j$ are joined by a polygonal line $ij$, the interior of one polygonal line is disjoint with any other polygonal line, the linking coefficient of any pair of disjoint 3-cycles except for $\{123,456\}$ is zero, and for the exceptional pair $\{123,456\}$ is $2z+1$. We prove a higher-dimensional analogue, which is a `converse' of a lemma by Segal-Spież.
