Kauffman's conjecture on detecting knot chirality by the Kauffman polynomial
Kauffman's conjecture on detecting knot chirality by the Kauffman polynomial
Let be a knot, let denote its mirror image, and let denote the mirror image with reversed orientation. The Kauffman polynomial of is denoted by . Kauffman's conjecture. If is not isotopic to its mirror image ( or ), then
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.
Progress summary
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