Equivalent characterizations of handle-ribbon knots [article]

Maggie Miller, Alexander Zupan
2020 arXiv   pre-print
The stable Kauffman conjecture posits that a knot in S^3 is slice if and only if it admits a slice derivative. We prove a related statement: A knot is handle-ribbon (also called strongly homotopy-ribbon) in a homotopy 4-ball B if and only if it admits an R-link derivative; i.e. an n-component derivative L with the property that zero-framed surgery on L yields #^n(S^1× S^2). We also show that K bounds a handle-ribbon disk D ⊂ B if and only if the 3-manifold obtained by zero-surgery on K admits a
more » ... singular fibration that extends over handlebodies in B ∖ D, generalizing a classical theorem of Casson and Gordon to the non-fibered case for handle-ribbon knots.
arXiv:2005.11243v1 fatcat:xafko2fayvenpjfmaozvd23gni