2020/05/22 by Maggie Miller, Miller, Maggie, Alexander Zupan +1
Mathematics · #57K10 #57K40 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2005.11243
openalex publication_date 2020/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The stable Kauffman conjecture posits that a knot in S3 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(S1× S2). 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 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.