9 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…
Unknotting number, ribbon concordance, and singular instantons
Hayato Imori, JungHwan Park, Masaki Taniguchi
We use equivariant singular instanton Floer theory with the Chern--Simons filtration to obstruct same-sign unknotting operations. We show that, for a large class of slice knots obt…
Forbidden configurations and definite fillings of lens spaces
Antony T. H. Fung, JungHwan Park
We study definite fillings of lens spaces. We classify the lens spaces for which every smooth negative-definite filling satisfies \[ b_2(X)\ge b_2(X(p,q))-1, \] where…
Equivariant lattice homology for Seifert homology 3-spheres
Sungkyung Kang, JungHwan Park, Masaki Taniguchi
We develop an -equivariant refinement of the lattice homotopy type for Seifert homology 3-spheres equipped with the Seifert -action. We const…
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…
A satellite formula for real Seiberg-Witten Floer homotopy types
Jin Miyazawa, JungHwan Park, Masaki Taniguchi
We establish a satellite formula for the real Seiberg-Witten Floer homotopy types of knots with odd patterns. Using this, we derive several applications to knot concordance theory.…
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…
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…
Doubled Disks and Satellite Surfaces
Gary Guth, Kyle Hayden, Sungkyung Kang +1
Conjecturally, a knot is slice if and only if its positive Whitehead double is slice. We consider an analogue of this conjecture for slice disks in the four-ball: two slice disks o…