The colored HOMFLY-PT polynomials of the trefoil knot, the figure-eight knot and twist knots

Abstract

We give a rigorous proof of the colored HOMFLY-PT polynomials of the trefoil knot, the figure-eight knot and twist knots. For the trefoil knot and the figure-eight knot, it is expressed by a single sum, and for a twist knot, it is expressed by a double sum.

20 pages, 20 figures

References in corpus (2)

• HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
• Large N Duality, Mirror Symmetry, and a Q-deformed A-polynomial for Knots

Cited by in corpus (1)

• Evolution properties of the knot's defect