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math.GT2024
Exotic Dehn twists and homotopy coherent group actions
Sungkyung Kang, JungHwan Park, Masaki Taniguchi
We consider the question of extending a smooth homotopy coherent finite cyclic group action on the boundary of a smooth 4-manifold to its interior. As a result, we prove that Dehn…
math.GT2024
Cables of the figure-eight knot via real Frøyshov invariants
Sungkyung Kang, JungHwan Park, Masaki Taniguchi
We prove that the -cable of the figure-eight knot is not smoothly slice when is odd, by using the real Seiberg-Witten Frøyshov invariant of Konno-Miyazawa-Taniguchi. Fo…
math.GT2024
Invariant splitting principles for the Lipshitz--Ozsváth--Thurston correspondence
Gary Guth, Sungkyung Kang
We prove that the Lipshitz-Ozsváth-Thurston correspondence between extended type D structures of knot complements and knot Floer complexes can be arranged s…