Some `converses' to intrinsic linking theorems

Abstract

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.

14 pages, no figures, exposition slightly improved

References in corpus (3)

• Hardness of almost embedding simplicial complexes in ${\mathbb{R}}^d$
• Extendability of simplicial maps is undecidable
• Some `converses' to intrinsic linking theorems

Cited by in corpus (1)

• Some `converses' to intrinsic linking theorems