Extending fibrations of knot complements to ribbon disk complements

Miller, Maggie¹

¹ Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, United States

Geometry & topology, Tome 25 (2021) no. 3, pp. 1479-1550.

Résumé

We show that if $K$ is a fibered ribbon knot in $S^3=\partial B^4$ bounding a ribbon disk $D$, 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 $S^1$.

Détail

DOI : 10.2140/gt.2021.25.1479

Keywords: fibered, ribbon, knot, slice, topology, 4-manifold

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