Twistings and the Alexander polynomial

2022/02/25 by Da‐Ren Chen, Chen, Daren
Mathematics · #17B37 #57K14 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2202.12489

openalex publication_date 2022/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit formula of the Alexander polynomial of the link obtained by adding an arbitrary number of full twists to positively oriented parallel n-strands in terms of the Alexander polynomials of the links obtained by adding 0,1,...,n-1 full twists. From this, we see that the Alexander polynomials stabilize after adding sufficiently many full twists. The main tool used in the computation is expressing the Alexander polynomial using the vector space representation of U_q(gl(1|1)).

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