We show that if is a fibered ribbon knot in bounding a ribbon disk , then, given an extra transversality condition, the fibration on extends to a fibration of . This partially answers a question of Casson and Gordon. In particular, we show the fibration always extends when has exactly two local minima. More generally, we construct movies of singular fibrations on –manifolds and describe a sufficient property of a movie to imply the underlying –manifold is fibered over .
"Extending fibrations of knot complements to ribbon disk complements." Geom. Topol. 25 (3) 1479 - 1550, 2021. https://doi.org/10.2140/gt.2021.25.1479