2024/02/02 by Ian Sullivan, Sullivan, Ian A., Melissa Zhang +1 · 2 citations
Mathematics · #57K18 (Primary) 57R56 #57K41 (Secondary) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2402.01081
openalex publication_date 2024/02/02 · openalex created_date 2024/02/06 · openalex updated_date 2026/07/28
We interpret Manolescu-Neithalath's cabled Khovanov homology formula for computing Morrison-Walker-Wedrich's KhR2 skein lasagna module as a homotopy colimit (mapping telescope) in a completion of the category of complexes over Bar-Natan's cobordism category. Using categorified projectors, we compute the KhR2 skein lasagna modules of (manifold, boundary link) pairs (S2 × B2, β), where β is a geometrically essential boundary link, identifying a relationship between the lasagna module and the Rozansky projector appearing in the Rozansky-Willis invariant for nullhomologous links in S2 × S1. As an application, we show that the KhR2 skein lasagna module of S2 × S2 is trivial, confirming a conjecture of Manolescu.