2020/08/06 by Роман Карасев, Karasev, R., Arkadiy Skopenkov +1 · 4 citations
Computer Science · Mathematics · #55S91 #57K45 #57Q35 #68U05 #Algebraic Topology (math.AT) #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2008.02523
openalex publication_date 2020/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A low-dimensional version of our main result is the following `converse' of the Conway-Gordon-Sachs Theorem on intrinsic linking of the graph K6 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.