Kauffman's conjecture on detecting knot chirality by the Kauffman polynomial

Let KK be a knot, let K\overline{K} denote its mirror image, and let K-\overline{K} denote the mirror image with reversed orientation. The Kauffman polynomial of KK is denoted by FK(a,z)F_K(a,z). Kauffman's conjecture. If KK is not isotopic to its mirror image (K\overline{K} or K-\overline{K}), then

FK(a,z)FK(a,z).F_K(a,z)\neq F_{\overline{K}}(a,z).

The conjecture asserts that the Kauffman polynomial detects chirality in knots, despite the invariant's general inability to distinguish some links from their mirror images. Its status is open in the supplied source context.

Sources & referencesView supporting material

Primary source

Jozef H. Przytycki, “Conway type invariants of links and Kauffman's method”, arXiv:1209.1592 (2012).

Additional references

2 papers in this index state this conjecture (2008–2012). The statement above is taken from the most recent of them; the others are arXiv:0810.4191.

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