Obviously the HOMFLY polynomial is a more superior invariant than the Jones polynomial since it is a geralisation of the Jones. However, are there knots that can be distinguished between by the Jones polynomial that the HOMFLY polynomial cannot distiguish?
2026-03-26 01:25:16.1774488316
Are there knots that can be distinguished between by the Jones polynomial that the HOMFLY polynomial cannot distiguish?
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No: as you mention, the HOMFLY polynomial specializes to the Jones polynomial, so if the HOMFLY polynomials of two knots are equal then their Jones polynomials must also be equal.