Work

A skein relation for singular Soergel bimodules

Year: 2026

Type: article

Abstract: 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 $$\mathfrak {sl}_{2}$$ .

Source: Selecta Mathematica

DOI: 10.1007/s00029-025-01121-x

Authors: Matthew Hogancamp, David E. V. Rose, Paul Wedrich

Institutions: Northeastern University, University of North Carolina at Chapel Hill, University of Bonn, Universität Hamburg, Max Planck Institute for Mathematics

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: National Science Foundation