Seungwon Kim

collaborators

5 papers

math.GT2026

Spanning solids and Murasugi sum in dimension four

Homayun Karimi, Seungwon Kim, Thomas Kindred +2

We study various constructions of spanning solids for knotted surfaces in the 4-sphere. In particular, we consider a 4-dimensional analogue of Murasugi sum, which we use to define…

math.GT2026

An irreducible real projective plane in the 4-sphere

Mark Hughes, Seungwon Kim, Maggie Miller +1

We construct an irreducible embedded projective plane in $S^{4}$ . This gives a counterexample to the Kinoshita conjecture and answers Problem 4.37 of the K3 problem list. Moreover, w…

math.GT2026

Knotting and linking in 4 and 5 dimensions from barbell diffeomorphisms

Seungwon Kim, Gheehyun Nahm, Alison Tatsuoka

In this paper, we construct infinitely many non-isotopic 3-knots in the 5-sphere, each of which has four critical points with respect to the standard height function of the 5-spher…

math.GT2026

Brunnian links of 3-balls in the 4-sphere

Seungwon Kim, Gheehyun Nahm, Alison Tatsuoka

For each integer $n \geq 2$ , we construct infinitely many $n$ -component Brunnian links of 3-balls in $S^{4}$ . Our main tool is the third author's result on the existence of splitting s…

math.GT2025

Branched covers of twist-roll spun knots and turned twisted tori

Mark Hughes, Seungwon Kim, Maggie Miller

We prove that the double branched cover of a twist-roll spun knot in $S^{4}$ is smoothly preserved when four twists are added, and that the double branched cover of a twist-roll spun…