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2021 Extending fibrations of knot complements to ribbon disk complements
Maggie Miller
Geom. Topol. 25(3): 1479-1550 (2021). DOI: 10.2140/gt.2021.25.1479

Abstract

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 S3ν(K) extends to a fibration of B4ν(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.

Citation

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Maggie Miller. "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

Information

Received: 28 February 2019; Revised: 3 June 2020; Accepted: 21 July 2020; Published: 2021
First available in Project Euclid: 19 July 2021

Digital Object Identifier: 10.2140/gt.2021.25.1479

Subjects:
Primary: 57K45, 57K99
Secondary: 57K10, 57K40

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.25 • No. 3 • 2021
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