2 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 . This gives a counterexample to the Kinoshita conjecture and answers Problem 4.37 of the K3 problem list. Moreover, w…