6 papers
Non-kinetic homotopy coherent actions on four-manifolds
Sungkyung Kang, JungHwan Park, Masaki Taniguchi
We give the first example of a non-kinetic smooth homotopy coherent action of order two on a closed simply connected smooth four-manifold. This action is obtained by restricting a…
Exotic diffeomorphisms on a contractible 4-manifold surviving two stabilizations
Sungkyung Kang, JungHwan Park, Masaki Taniguchi
We develop a -equivariant refinement of the lattice homotopy type for computing equivariant Seiberg--Witten Floer homotopy types. As an applica…
Smooth concordance of cables of the figure-eight knot
Sungkyung Kang, JungHwan Park, Masaki Taniguchi
We prove that every nontrivial cable of the figure-eight knot has infinite order in the smooth knot concordance group. Our main contribution is a uniform proof that applies to all…
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. F…
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…
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…