TY - JOUR
T1 - Gompf’s Cork and Heegaard Floer Homology
AU - Dai, Irving
AU - Mallick, Abhishek
AU - Zemke, Ian
N1 - Publisher Copyright:
© The Author(s) 2024. Published by Oxford University Press. All rights reserved.
PY - 2024/9/1
Y1 - 2024/9/1
N2 - 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.
AB - 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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U2 - 10.1093/imrn/rnae180
DO - 10.1093/imrn/rnae180
M3 - Article
AN - SCOPUS:85204984739
SN - 1073-7928
VL - 2024
SP - 12663
EP - 12682
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 18
ER -