2025/04/04 by Ian Sullivan, Sullivan, Ian A.
Mathematics · #57K41 (Primary) 57K18 #57R55 #57R56 (Secondary) #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2504.03968
openalex publication_date 2025/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct and study the skein lasagna module obtained by importing the Bar-Natan Khovanov homology package. For 4-manifolds satisfying a non-vanishing condition, we produce pairs of exotic surfaces (with boundary) by using the behavior of skein lasagna gluing maps associated to connect sums of 4-manifolds. We show that one internal stabilization is generally not enough for these exotic knotted surfaces, generalizing results of Hayden to 4-manifolds that contain homologically diverse surfaces admitting primitive fillings.