An Alexander polynomial for MOY graphs

• Yuanyuan Bao ^[1] ; Zhongtao Wu ^[2]
  1. [1] University of Tokyo

     University of Tokyo

     Japón

     
  2. [2] The Chinese University of Hong Kong, China
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 2, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-020-00556-8
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• Resumen

  • We introduce an Alexander polynomial for MOY graphs. For a framed trivalent MOY graph G, we refine the construction and obtain a framed ambient isotopy invariant Δ(G,c)(t). The invariant Δ(G,c)(t) satisfies a series of relations, which we call MOY-type relations, and conversely these relations determine Δ(G,c)(t). Using them we provide a graphical definition of the Alexander polynomial of a link. Finally, we discuss some properties and applications of our invariants.