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Bar-Natan skein lasagna modules and exotic surfaces in 4-manifolds

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arxiv 2504.03968 v2 pith:L4GBS2EQ submitted 2025-04-04 math.GT

Ian A. Sullivan This is my paper · ORCID
classification math.GT
keywords manifoldssurfacesexoticlasagnaskeinbar-natanadmittingassociated
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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.

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  1. From Link Homology to Topological Quantum Field Theories

    math.QA 2025-09 accept novelty 2.0 of 10

    A survey of how link homology theories extend to 4-manifold invariants called skein lasagna modules, which can distinguish exotic smooth structures.

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