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<p>We employ the reduced Burau representation of the braid group to compute the Alexander polynomial and verify Fox’s Trapezoidal Conjecture for certain families of generalized weaving links with three and four strands. Furthermore, we propose an approach to addressing the conjecture for closed alternating braids by analyzing the reduced Burau representation.</p>

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Attacks on Fox’s Trapezoidal Conjecture

  • 期刊论文

  • 发表日期：

    2026年3月28日

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  • Mohamad N. Nasser,
  • Taher I. Mayassi,
  • Nafaa Chbili

摘要

We employ the reduced Burau representation of the braid group to compute the Alexander polynomial and verify Fox’s Trapezoidal Conjecture for certain families of generalized weaving links with three and four strands. Furthermore, we propose an approach to addressing the conjecture for closed alternating braids by analyzing the reduced Burau representation.