Linking invariants of spatial graphs

E. Alkin; Yu. Khromin; A. Skopenkov

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arXiv · 2608.15860

Linking invariants of spatial graphs

E. Alkin·Yu. Khromin·A. Skopenkov

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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.

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BibTeX RIS

E. Alkin, Yu. Khromin, A. Skopenkov. 2026-08-16. Linking invariants of spatial graphs. https://arxiv.org/abs/2608.15860

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