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Extending fibrations of knot complements to ribbon disk complements

Maggie Miller

Geometry & Topology 25 (2021) 1479–1550

We show that if K is a fibered ribbon knot in S3 = B4 bounding a ribbon disk D, then, given an extra transversality condition, the fibration on S3 ν(K) extends to a fibration of B4 ν(D). 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 S1.

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fibered, ribbon, knot, slice, topology, 4-manifold
Mathematical Subject Classification
Primary: 57K45, 57K99
Secondary: 57K10, 57K40
Received: 28 February 2019
Revised: 3 June 2020
Accepted: 21 July 2020
Published: 20 May 2021
Proposed: Cameron Gordon
Seconded: Mladen Bestvina, Ciprian Manolescu
Maggie Miller
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States