Gompf’s Cork and Heegaard Floer Homology

Irving Dai, Abhishek Mallick, Ian Zemke

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)12663-12682
Number of pages20
JournalInternational Mathematics Research Notices
Volume2024
Issue number18
DOIs
StatePublished - Sep 1 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics

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