English

The Reidemeister graph is a complete knot invariant

Geometric Topology 2020-04-29 v1

Abstract

We describe two locally finite graphs naturally associated to each knot type K, called Reidemeister graphs. We determine several local and global properties of these graphs and prove that in one case the graph-isomorphism type is a complete knot invariant up to mirroring. Lastly, we introduce another object, relating the Reidemeister and Gordian graphs, and determine some of its properties.

Keywords

Cite

@article{arxiv.1801.03313,
  title  = {The Reidemeister graph is a complete knot invariant},
  author = {Agnese Barbensi and Daniele Celoria},
  journal= {arXiv preprint arXiv:1801.03313},
  year   = {2020}
}

Comments

49 pages, 51 figures. Comments are welcome!

R2 v1 2026-06-22T23:41:27.635Z