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

2021/07/19 by Kenichi Kawagoe, Kawagoe, Kenichi · 1 citation
Mathematics · #57M25 #57M27 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2107.08678

openalex publication_date 2021/07/19 · openalex created_date 2021/08/02 · openalex updated_date 2026/07/28

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.

Citations

• Large N Duality, Mirror Symmetry, and a Q-deformed A-polynomial for Knots

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