#### Volume 25, issue 3 (2021)

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Extending fibrations of knot complements to ribbon disk complements

### Maggie Miller

Geometry & Topology 25 (2021) 1479–1550
##### Abstract

We show that if $K$ is a fibered ribbon knot in ${S}^{3}=\partial {B}^{4}$ bounding a ribbon disk $D\phantom{\rule{-0.17em}{0ex}}$, then, given an extra transversality condition, the fibration on ${S}^{3}\setminus \nu \left(K\right)$ extends to a fibration of ${B}^{4}\setminus \nu \left(D\right)$. This partially answers a question of Casson and Gordon. In particular, we show the fibration always extends when $D$ has exactly two local minima. More generally, we construct movies of singular fibrations on $4$–manifolds and describe a sufficient property of a movie to imply the underlying $4$–manifold is fibered over ${S}^{1}$.

##### Keywords
fibered, ribbon, knot, slice, topology, 4-manifold
##### Mathematical Subject Classification
Primary: 57K45, 57K99
Secondary: 57K10, 57K40