knot inv comparison
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  • Homology
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  • Ballmapper
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Select invariants to compare their ballmappers. Input has selectable nodes, which is compared to Output by pressing the [Compare!] button.

Note:

  • Everything is for knots up to 16 crossings; except HOMFLYPTHomology (3-11 crossings) and KR3 (3-15) crossings.
  • Everything is normalised with ballmapper ; except for A2 and HOMFLYPTHomology with .
  • HOMFLYPTHomology was calculated over knots in a different order, so do not expect comparisons to work with it.

Interactive plot: zoom, pan, hover and select!

  • Size of nodes (barely) indicates how many knots inside.
  • Hover over nodes to see their indexing and coverage (for comparison ballmapper). Color of nodes indicate percentage of knots selected. Nodes are semi-transparent so their color is not completely accurate when overlapping. To see which knots live inside each node, see [A2, Alexander, B1, HFK2, HFK2T1, HOMFLYPT, HOMFLYPTHomology, Jones, Khovanov, KhovanovT1, KhovanovOdd, KR3].

Toggle lasso selection on the first ballmapper. For your convenience, holding [Ctrl] or [Shift] keys will temporarily switch between pan and lasso mode.

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