The Rasmussen s-invariant and exotic 4-manifolds

Gheehyun Nahm

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arXiv · 2602.20138

The Rasmussen s-invariant and exotic 4-manifolds

Gheehyun Nahm

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Abstract

We give a short, analysis-free proof, inspired by Ren and Willis's, of the existence of exotic compact, orientable 4-manifolds. There are two distinguishing features of our proof. First, we avoid skein lasagna modules; we use Beliakova and Wehrli's generalization of Rasmussen's s-invariant to links in $S^{3}$ directly. Second, we reduce the complexity of the computations by choosing clever induction hypotheses in Sto\v{s}i\'{c}'s induction scheme; this in particular allows us to avoid Ren and Willis's Comparison Lemma.

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Gheehyun Nahm. 2026-02-23. The Rasmussen s-invariant and exotic 4-manifolds. https://arxiv.org/abs/2602.20138

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