Skip navigation
Please use this identifier to cite or link to this item:
Title: Extending fibrations of knot complements to ribbon disk complements
Authors: Miller, Maggie
Advisors: Gabai, David
Contributors: Mathematics Department
Keywords: 4-manifold
Subjects: Mathematics
Issue Date: 2020
Publisher: Princeton, NJ : Princeton University
Abstract: We show that if K is a fibered ribbon knot in S^3=(boundary B^4) bounding ribbon disk D, then with a transversality condition the fibration on the complement of K in S^3 extends to a fibration of the complement of D in B^4. This partially answers a question of Casson and Gordon (``If D is a homotopy-ribbon disk bounded by a fibered knot, is D fibered?"). In particular, we show the fibration always extends when D has exactly two local minima, extending a result of Scharlemann for the unknot. 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.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

Files in This Item:
File Description SizeFormat 
Miller_princeton_0181D_13294.pdf2.13 MBAdobe PDFView/Download

Items in Dataspace are protected by copyright, with all rights reserved, unless otherwise indicated.