2020/09/07 by Onkar Singh Gujral, Gujral, Onkar Singh, Adam Simon Levine +1 · 1 citation
Mathematics · Medicine · #57K10 #57K18 #57K45 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2009.03406
openalex publication_date 2020/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the (in)sensitivity of the Khovanov functor to four-dimensional linking of surfaces. We prove that if L and L' are split links, and C is a cobordism between L and L' that is the union of disjoint (but possibly linked) cobordisms between the components of L and the components of L', then the map on Khovanov homology induced by C is completely determined by the maps induced by the individual components of C and does not detect the linking between the components. As a corollary, we prove that a strongly homotopy-ribbon concordance (i.e., a concordance whose complement can be built with only 1- and 2-handles) induces an injection on Khovanov homology, which generalizes a result of the second author and Zemke. Additionally, we show that a non-split link cannot be ribbon concordant to a split link.