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.
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页数：7
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