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Tail of the Jones Polynomial Heatmaps

Visualizations of the tail of the colored Jones polynomials and colored \(\mathfrak{sl}_N\) polynomials.

  • x axis: even q powers
  • y axis: jth colored Jones polynomial normalized by the lowest q power and so that the constant term is positive.
  • heatmap: coefficient of monomials, where orange is +1, green is -1, red is > 1, and blue is < 1

Note that because of this color scheme, the color bar is often a bit buggy. Additionally, we plot a staircase that shows the highest stable q power for each polynomial.

sl2 tail of K_5/2

Tail of Jones polynomial for \(K_{5/2}\).

sl3 tail of K_5/2

Tail of \(\mathfrak{sl}_3\) polynomial for \(K_{5/2}\).

sl4 tail of K_5/2

Tail of \(\mathfrak{sl}_4\) polynomial for \(K_{5/2}\).

sl5 tail of K_5/2

Tail of \(\mathfrak{sl}_5\) polynomial for \(K_{5/2}\).

sl2 tail of K_7/3

Tail of Jones polynomial for \(K_{7/3}\).

sl3 tail of K_7/3

Tail of \(\mathfrak{sl}_3\) polynomial for \(K_{7/3}\).

sl4 tail of K_7/3

Tail of \(\mathfrak{sl}_4\) polynomial for \(K_{7/3}\).

sl5 tail of K_7/3

Tail of \(\mathfrak{sl}_5\) polynomial for \(K_{7/3}\).