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math.GT2026
Unknotting orientable surfaces
Anthony Conway
It is shown that every locally flatly embedded genus surface in the -sphere with knot group is unknotted. The same proof establishes that any two ge…
math.GT2026
Non-smoothable surfaces in the 4-sphere
Anthony Conway, Daniel Galvin
We construct examples of non-smoothable surfaces in the -sphere, thereby answering Question 4.32 on the K3 problem list. These surfaces are non-orientable and have knot group of…