There exist no minimally knotted planar spatial graphs on the torus

被引：2

作者：

Barthel, Senja ^{[1
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, London SW7 2AZ, England

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2015年 / 24卷 / 07期

关键词：

Topological graphs; knots and links; topology and chemistry; chirality; templating on a toroidal substrate;

D O I：

10.1142/S0218216515500352

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that all nontrivial embeddings of planar graphs on the torus contain a nontrivial knot or a nonsplit link. This is equivalent to showing that no minimally knotted planar spatial graphs on the torus exist that contain neither a nontrivial knot nor a nonsplit link all of whose components are unknots.

引用

页数：7

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