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math.GT2025
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…
math.GT2025
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…
math.GT2025
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.…