The Last Three T-degrees in Triply-Graded Link Homology

2025/05/20 by Cailan Li, Li, Cailan · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2505.14182

openalex publication_date 2025/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the structure of reduced triply graded link homology HHH in the top/bottom three T-degrees for links arising as closures of positive/negative braids. Using a diagrammatic approach to the Hochschild cohomology of Soergel bimodules, we provide explicit computations of HHH as R-modules in these degrees. Our results reveal that the homology here is often zero, especially in the negative braid case, and display striking uniformity.

Citations

• The Two-Color Ext Soergel Calculus
• Path isomorphisms between quiver Hecke and diagrammatic Bott-Samelson endomorphism algebras
• Serre duality for Khovanov–Rozansky homology
• Koszul duality for Kac-Moody groups and characters of tilting modules
• The anti-spherical category
• Schubert calculus and torsion explosion
• Categorification of the braid groups

Cited by

• Serre Duality and the Whitehead Link

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