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

Ian A. Sullivan

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arXiv · 2504.03968

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

Ian A. Sullivan

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Abstract

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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Ian A. Sullivan. 2025-04-04. Bar-Natan skein lasagna modules and exotic surfaces in 4-manifolds. https://arxiv.org/abs/2504.03968

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