Toroidal embeddings of abstractly planar graphs are knotted or linked

Senja Barthel; Dorothy Buck

doi:10.1007/s10910-015-0519-1

Toroidal embeddings of abstractly planar graphs are knotted or linked

Senja Barthel^*
, Dorothy Buck

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

We give explicit deformations of embeddings of abstractly planar graphs that lie on the standard torus $$T^2 \subset \mathbb {R}^3$$^T2⊂^R3 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.

Original language	English
Pages (from-to)	1772-1790
Number of pages	19
Journal	Journal of Mathematical Chemistry
Volume	53
Issue number	8
DOIs	https://doi.org/10.1007/s10910-015-0519-1
Publication status	Published - 13 Sept 2015
Externally published	Yes

Keywords

Knots and links
Templating on a toroidal substrate
Topological graphs

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10.1007/s10910-015-0519-1

https://arxiv.org/abs/1505.05696v2

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title = "Toroidal embeddings of abstractly planar graphs are knotted or linked",

abstract = "We give explicit deformations of embeddings of abstractly planar graphs that lie on the standard torus \$\$T\textasciicircum{}2 \textbackslash{}subset \textbackslash{}mathbb \{R\}\textasciicircum{}3\$\$T2⊂R3 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.",

keywords = "Knots and links, Templating on a toroidal substrate, Topological graphs",

author = "Senja Barthel and Dorothy Buck",

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doi = "10.1007/s10910-015-0519-1",

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journal = "Journal of Mathematical Chemistry",

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T1 - Toroidal embeddings of abstractly planar graphs are knotted or linked

AU - Barthel, Senja

AU - Buck, Dorothy

PY - 2015/9/13

Y1 - 2015/9/13

N2 - We give explicit deformations of embeddings of abstractly planar graphs that lie on the standard torus $$T^2 \subset \mathbb {R}^3$$T2⊂R3 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.

AB - We give explicit deformations of embeddings of abstractly planar graphs that lie on the standard torus $$T^2 \subset \mathbb {R}^3$$T2⊂R3 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.

KW - Knots and links

KW - Templating on a toroidal substrate

KW - Topological graphs

UR - https://www.scopus.com/pages/publications/84938993125

UR - https://www.scopus.com/pages/publications/84938993125#tab=citedBy

U2 - 10.1007/s10910-015-0519-1

DO - 10.1007/s10910-015-0519-1

M3 - Article

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SP - 1772

EP - 1790

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

IS - 8

ER -

Toroidal embeddings of abstractly planar graphs are knotted or linked

Abstract

Keywords

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