2022/10/11 by Matthew Hogancamp, Hogancamp, Matthew, David E. V. Rose +3 · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2210.05640
openalex publication_date 2022/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a Kirby color in the setting of Khovanov homology: an ind-object of the annular Bar-Natan category that is equipped with a natural handle slide isomorphism. Using functoriality and cabling properties of Khovanov homology, we define a Kirby-colored Khovanov homology that is invariant under the handle slide Kirby move, up to isomorphism. Via the Manolescu--Neithalath 2-handle formula, Kirby-colored Khovanov homology agrees with the \mathfrakgl2 skein lasagna module, hence is an invariant of 4-dimensional 2-handlebodies.