Quotients of the Gordian and H(2)-Gordian graphs

@article{Flippen2021QuotientsOT,
  title={Quotients of the Gordian and H(2)-Gordian graphs},
  author={Christopher Flippen and Allison H. Moore and Essak Seddiq},
  journal={Journal of Knot Theory and Its Ramifications},
  year={2021},
  volume={30},
  pages={2150037}
}
The Gordian graph and H(2)-Gordian graphs of knots are abstract graphs whose vertex sets represent isotopy classes of unoriented knots, and whose edge sets record whether pairs of knots are related by crossing changes or H(2)-moves, respectively. We investigate quotients of these graphs under equivalence relations defined by several knot invariants including the determinant, the span of the Jones polynomial, and an invariant related to tricolorability. We show, in all cases considered, that the… Expand

Figures from this paper

References

SHOWING 1-10 OF 53 REFERENCES
Knot Graphs and Gromov Hyperbolicity
We define three types of knot graphs, constructed with the help of unknotting operations, the concordance relation and knot invariants. Some of these graphs have been previously studied in theExpand
SoC
  • 友紀子 中川
  • Journal of Japan Society for Fuzzy Theory and Intelligent Informatics
  • 2021
KEY: # = new course * = course changed † = course dropped University of Kentucky 2014-2015 Undergraduate Bulletin 1 SOC 10
Cambridge Philos
  • Soc., 169(1):141–148,
  • 2020
Knotinfo: Table of knot invariants
  • URL: knotinfo.math.indiana.edu, June
  • 2020
Symmetric quotients of knot groups and a filtration of the Gordian graph
Abstract We define a metric filtration of the Gordian graph by an infinite family of 1-dense subgraphs. The nth subgraph of this family is generated by all knots whose fundamental groups surject to aExpand
27(9):1842002
  • 6,
  • 2018
A bridge between Conway–Coxeter friezes and rational tangles through the Kauffman bracket polynomials
In the present paper, we build a bridge between Conway-Coxeter friezes and rational tangles through the Kauffman bracket polynomials. One can compute a Kauffman bracket polynomials attached toExpand
A note on the Gordian complexes of some local moves on knots
In this paper, the [Formula: see text]-move is defined. We show that for any knot [Formula: see text], there exists an infinite family of knots [Formula: see text] such that the Gordian distanceExpand
Topology
The H(n)-Gordian complex of knots
In this paper, the H(n)-Gordian complex of knots is defined. The authors show that for any knot K and any positive integer r, there is a finite set of knots of size r containing K, such that the H(...
...
1
2
3
4
5
...