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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
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 , we construct infinitely many -component Brunnian links of 3-balls in . Our main tool is the third author's result on the existence of splitting s…