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  1. ; ; (, International Mathematics Research Notices)
    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. 
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  2. ; ; (, Journal of Topology)
    Abstract We define several equivariant concordance invariants using knot Floer homology. We show that our invariants provide a lower bound for the equivariant slice genus and use this to give a family of strongly invertible slice knots whose equivariant slice genus grows arbitrarily large, answering a question of Boyle and Issa. We also apply our formalism to several seemingly nonequivariant questions. In particular, we show that knot Floer homology can be used to detect exotic pairs of slice disks, recovering an example due to Hayden, and extend a result due to Miller and Powell regarding stabilization distance. Our formalism suggests a possible route toward establishing the noncommutativity of the equivariant concordance group. 
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  3. ; ; ; (, Mathematische Annalen)
    Free, publicly-accessible full text available December 1, 2025