The HOMFLY-PT and Kauffman polynomials satisfy a previously torus-only relation for several infinite hyperbolic knot families that have factorised Harer-Zagier transforms.
Jones, Hecke algebra representations of braid groups and link poly- nomials, Annals of Mathematics 126 (1987) 335
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The HOMFLY-PT polynomial and HZ factorisation
The HOMFLY-PT and Kauffman polynomials satisfy a previously torus-only relation for several infinite hyperbolic knot families that have factorised Harer-Zagier transforms.