Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01w6634654p
 Title: Extending fibrations of knot complements to ribbon disk complements Authors: Miller, Maggie Advisors: Gabai, David Contributors: Mathematics Department Keywords: 4-manifoldfibrationknotribbonslicetopology 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. URI: http://arks.princeton.edu/ark:/88435/dsp01w6634654p Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: catalog.princeton.edu Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Mathematics