Knot invariants and their relations: a topological perspective


This page contains accompagning and additional interactive plots for P. Dłotko, D. Gurnari, and R. Sazdanovic, Mapper-type algorithms for complex data and relations (2024) DOI 10.1080/10618600.2024.2343321. All data and code can be found at DOI 10.5281/zenodo.10876347.

3d visualization of the space of Jones polynomials for all knots up to 15 crossings colored by signature.


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.
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.
KnotInfo BallMapper graphs
Interactive graphs of the space of different knots polynomials, constructed from the data publicly available at KnotInfo. Different coloring functions can be choosen using the drop-down menu. Code to recreate (and inspect) these graphs can be found on this repository.