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Abstract Gompf showed that for K in a certain family of double-twist knots, the swallow-follow operation makes 1/n-surgery on K \# -K into a cork boundary. We derive a general Floer-theoretic condition on K under which this is the case. Our formalism allows us to produce many further examples of corks, partially answering a question of Gompf. Unlike Gompf’s method, our proof does not rely on any closed 4-manifold invariants or effective embeddings, and also generalizes to other diffeomorphisms.
Dai et al. (Thu,) studied this question.
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