Knot invariants and their relations: a topological perspective

This page contains accompagning and additional interactive plots for arXiv:2109.00831.
The full list of figures in the paper can be found here.


Below some additional interactive examples can be found. All graphs can be zoomed in and saved to png using the icons in the toolbar.

BallMapper graphs
Interactive graphs of the space of different knots polynomials. Different coloring functions can be choosen using the drop-down menu.
  • Alexander BM
  • Jones BM
  • HOMFLY-PT BM
  • Khovanov BM

  • Maps between BallMapper graphs
    Examples of how knots in some clusters in a BallMapper graph are mapped into another BallMapper graph of different polynomials coefficients of the same sets of knots. Cluster in the left-hand side graph can be selected either by clicking or using the drop-down list. The COLOR button colors the right-hand graph by assigning to each of the nodes the percentage of its covered knots that are covered by the subset of nodes selected in the left-hand graph.
  • Alexander to Jones
  • Jones to HOMFLY-PT
  • Jones to Khovanov