English

There exist no Minimally Knotted Planar Spatial Graphs on the Torus

Geometric Topology 2019-05-06 v3

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.

Keywords

Cite

@article{arxiv.1411.7734,
  title  = {There exist no Minimally Knotted Planar Spatial Graphs on the Torus},
  author = {Senja Barthel},
  journal= {arXiv preprint arXiv:1411.7734},
  year   = {2019}
}

Comments

4 pages, 1 figure

R2 v1 2026-06-22T07:14:43.804Z