There exist no minimally knotted planar spatial graphs on the torus

Senja Barthel*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

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.

Original languageEnglish
Article number1550035
JournalJournal of Knot Theory and its Ramifications
Volume24
Issue number7
DOIs
Publication statusPublished - 3 Jun 2015
Externally publishedYes

Keywords

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

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