Sungkyung Kang

collaborators

4 papers

math.GT2026

Satellites and telescopes: a concordance formula for bordered Floer homology

Gary Guth, Sungkyung Kang

Given a knot $K$ in $S^{3}$ , its knot Floer completely determines the bordered Floer homology of its complement by a work of Lipshitz--OzsvÃ¡th--Thurston. Furthermore, the determinat…

math.GT2024

One stabilization is not enough for contractible 4-manifolds

Sungkyung Kang

We construct an example of a cork that remains exotic after taking a connected sum with $S^{2} \times S^{2}$ . Combined with a work of Akbulut-Ruberman, this implies the existence of an…

math.GT2024

The $(2, 1)$ -cable of the figure-eight knot is not smoothly slice

Irving Dai, Sungkyung Kang, Abhishek Mallick +2

We prove that the $(2, 1)$ -cable of the figure-eight knot is not smoothly slice by showing that its branched double cover bounds no equivariant homology ball.

math.GT2024

On the nonorientable four-ball genus of torus knots

Fraser Binns, Sungkyung Kang, Jonathan Simone +1

The nonorientable four-ball genus of a knot $K$ in $S^{3}$ is the minimal first Betti number of nonorientable surfaces in $B^{4}$ bounded by $K$ . By amalgamating ideas from involutive…

Satellites and telescopes: a concordance formula for bordered Floer homology

One stabilization is not enough for contractible 4-manifolds

The (2,1)-cable of the figure-eight knot is not smoothly slice

On the nonorientable four-ball genus of torus knots

The $(2, 1)$ -cable of the figure-eight knot is not smoothly slice