9 papers
-cobordisms, infinite cyclic covers, and real Seiberg--Witten theory
Sungkyung Kang, JungHwan Park, Masaki Taniguchi
We study -cobordisms of distinguished homology handles, introduced by Kawauchi in 1976 using infinite cyclic covers. Despite the extensive development of gauge-theor…
Real Floer Homotopy Types and -Invariants
Yoshihiro Fukumoto, Masaki Taniguchi
We express the local-equivalence classes of real Seiberg--Witten Floer homotopy types for spin Seifert -manifolds with certain odd involutions in terms of the Fukumoto-Furuta $w…
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…
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.…
On the connected sums of the -cable of the figure eight knot
Yoshihiro Fukumoto, Masaki Taniguchi
We show that the 3-fold (resp. 6-fold) connected sum of the -cable of the figure-eight knot cannot bound a smooth null-homologous disk in a punctured (resp.…
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…