Toroidal embeddings of abstractly planar graphs are knotted or linked

Senja Barthel; Dorothy Buck

doi:10.1007/s10910-015-0519-1

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arXiv · 1505.05696

Toroidal embeddings of abstractly planar graphs are knotted or linked

Senja Barthel·Dorothy Buck

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Abstract

We give explicit deformations of embeddings of abstractly planar graphs that lie on the standard torus $T^2 \subset \mathbb{R}^3$ and that contain neither a nontrivial knot nor a nonsplit link into the plane. It follows that ravels do not embed on the torus. Our results provide general insight into properties of molecules that are synthesized on a torus.

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Senja Barthel, Dorothy Buck. 2019-05-07. Toroidal embeddings of abstractly planar graphs are knotted or linked. https://doi.org/10.1007/s10910-015-0519-1

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