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math.GT2023
Doubled Disks and Satellite Surfaces
Gary Guth, Kyle Hayden, Sungkyung Kang +1
Conjecturally, a knot is slice if and only if its positive Whitehead double is slice. We consider an analogue of this conjecture for slice disks in the four-ball: two slice disks o…
math.GT2023
One stabilization is not enough for closed knotted surfaces
Kyle Hayden, Sungkyung Kang, Anubhav Mukherjee
In this brief note, we show that there exist smooth 4-manifolds (with nonempty boundary) containing pairs of exotically knotted 2-spheres that remain exotic after one (either exter…
math.GT2023
An atomic approach to Wall-type stabilization problems
Kyle Hayden
Wall-type stabilization problems investigate the collapse of exotic 4-dimensional phenomena under stabilization operations (e.g., taking connected sums with ). We p…