Negative amphichiral knots and the half-Conway polynomial

• Keegan Boyle ^[1] ; Wenzhao Chen ^[1]
  1. [1] University of British Columbia

     University of British Columbia

     Canadá

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 2, 2024, págs. 581-622
• Idioma: inglés
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• Resumen

  • In 1979, Hartley and Kawauchi proved that the Conway polynomial of a strongly negative amphichiral knot factors as f(z)f(−z). In this paper, we normalize the factor f(z) to define the half-Conway polynomial. First, we prove that the half-Conway polynomial satisfies an equivariant skein relation, giving the first feasible computational method, which we use to compute the half-Conway polynomial for knots with 12 or fewer crossings...