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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
Bridge position of 3-manifolds embedded in the 5-sphere
Román Aranda, Sarah Blackwell, Geunyoung Kim +2
We introduce and study bridge decompositions for 3-manifolds embedded in the 5-sphere. These generalize both the classical notion of bridge position for knots in the 3-sphere and t…