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 language | English |
|---|---|
| Article number | 1550035 |
| Journal | Journal of Knot Theory and its Ramifications |
| Volume | 24 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 3 Jun 2015 |
| Externally published | Yes |
Funding
I thank Tom Coates, Erica Flapan, Youngsik Huh, Stephen Hyde, Danielle O’Donnol, Makoto Ozawa, Matt Rathbun and Kouki Taniyama for helpful comments and discussions. I also want to thank my Ph.D. supervisor Dorothy Buck under whose supervision the research was undertaken. It was financially supported by the Roth studentship of Imperial College London Mathematics Department, the DAAD, the Evangelisches Studienwerk, the Doris Chen award, and by a JSPS Grant awarded to Kouki Taniyama.
Keywords
- chirality
- knots and links
- templating on a toroidal substrate
- Topological graphs
- topology and chemistry
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