Some `converses' to intrinsic linking theorems

08/06/2020

∙

by   R. Karasev, et al.

∙

0

∙

share

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 joint by a polygonal line ij, the interior of one polygonal line is disjoint with any other polygonal line, the linking coefficient of any pair 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.