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I'm wondering if its ever possible to find two non-isotopic knots which have identical jones polynomials but different seifert genus?

Attempting to google for this I found this example of non-isotopic knots with identical jones polynomials. But in the first page of the paper its clearly stated that all the knots have identical genus.

Sidharth Ghoshal
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  • This has been asked here where indeed a counter example was found: https://mathoverflow.net/questions/456521/are-there-examples-of-different-knots-with-identical-jones-polynomials-and-diffe – Sidharth Ghoshal Oct 16 '23 at 15:57

1 Answers1

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The Conway knot and Kinoshita-Teraska knot are mutants, so they share the same Jones polynomial. But the Conway knot has genus 3 and the Kinoshita-Terasaka knot has genus 2.

Agol
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