Serre Duality and the Whitehead Link

2025/09/26 by Li, Cailan
#FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2509.22133

Abstract

We prove the action of the full twist is a Serre functor in the homotopy category of dihedral Soergel Bimodules. Our proof relies on the representability of a certain partial trace functor, which we prove using the diagrammatics for Hochschild cohomology of Soergel Bimodules. Leveraging these representability results, we then compute the triply-graded link homology of the Whitehead link.

Citations

• The Last Three T-degrees in Triply-Graded Link Homology
• Relative Serre duality for Hecke categories
• Serre duality for Khovanov–Rozansky homology
• Gaitsgory's central sheaves via the diagrammatic Hecke category
• Categorification of the braid groups
• Braid group actions on derived categories of coherent sheaves

Related

• Soergel Bimodules, the Steenrod Algebra and Triply Graded Link homology
• The Two-Color Ext Soergel Calculus
• Derived traces of Soergel categories
• Virtual crossings and a filtration of the triply graded homology of a\n link diagram
• A skein relation for singular Soergel bimodules