A skein relation for singular Soergel bimodules

• Matthew Hogancamp ^[1] ; David E. V. Rose
  1. [1] Northeastern University, Boston,USA
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 32, Nº. 2, 2026
• Idioma: inglés
• DOI: 10.1007/s00029-025-01121-x
• Enlaces
  • Texto completo
• Resumen

  • We study the skein relation that governs the HOMFLYPT invariant of links colored by one-column Young diagrams. Our main result is a categorification of this colored skein relation. This takes the form of a homotopy equivalence between two one-sided twisted complexes constructed from Rickard complexes of singular Soergel bimodules associated to braided webs. Along the way, we prove a conjecture of Beliakova–Habiro relating the colored 2-strand full twist complex with the categorical ribbon element for quantum sl2.

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