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Ribbonness of Surface-Bounding Classical Links in the Upper Half 4-Space

A result and its proof in geometric topology showing that if a classical link in 3-space bounds a compact oriented proper surface (with no closed components) in the upper half of 4-space, then it also bounds a ribbon surface there, realized as a boundary-relative renewal embedding of that surface. The proof is built from banded loop systems and surgery on trivial sphere-links along handle systems, and the construction is shown invariant under isotopies respecting its arcs and loops.

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Alternative proof of the ribbonness on classical link Akio Kawauchi

A geometric-topology paper giving an alternative proof that a classical link which bounds a compact oriented proper surface (with no closed components) pushed into the upper half of 4-space must also…