Three thousand obstructions to knotless embedding

Thomas W Mattman; Andrei Pavelescu

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arXiv · 2607.01414

Three thousand obstructions to knotless embedding

Thomas W Mattman·Andrei Pavelescu

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Abstract

We present a list of 3028 obstructions to knotless embedding. We survey recent work in this area including: 1) A bibliography of graphs proven to be intrinsically knotted without relying on computers; 2) An updated listing of obstructions in $\nabla\mathrm{Y}$ families including two new large families; 3) Connections with the Colin de Verdi\`ere's invariant including a new obstruction with $\mu = 6$; and 4) Connectivity of obstructions and their structure near vertices of degree three or four. We address questions raised in earlier work, (re)state several conjectures, and propose new questions.

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Thomas W Mattman, Andrei Pavelescu. 2026-07-01. Three thousand obstructions to knotless embedding. https://arxiv.org/abs/2607.01414

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