Linking invariants of spatial graphs

Abstract

We recall definitions of linking numbers and Wu--Simon numbers for spatial graphs. We expose a `converse' to the Conway--Gordon--Sachs theorem (i.e. description of linking functions for embeddings $K_6\to {\mathbb{R}}^3$), and some results on Wu--Simon numbers. We conjecture and discuss a generalization of the Conway--Gordon--Sachs theorem to multiple linking. The exposition is based on plane diagrams, so no knowledge of spatial geometry is required.

17 pages (English) + 14 pages (Russian); many figures. The paper belongs to math.GT because the most closely related papers are arXiv:2006.07342 [math.GT], arXiv:2001.01472 [math.GT], arXiv:2410.09860 [math.GT], arXiv:1805.10237 [math.GT], arXiv:2205.01013 [math.GT]