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https://hdl.handle.net/2142/22501
Description
Title
Enumeration and classification of ribbon knots
Author(s)
Brown, Scott Allen
Issue Date
1995
Doctoral Committee Chair(s)
Haken, Wolfgang
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
A ribbon knot is one which bounds a certain type of singular disk in the 3-sphere. In this work we investigate an enumeration procedure for such disks and study a natural topological grouping of related ribbons which differ by twists along imbedded bands. When the knots under consideration possess a hyperbolic structure, we use a limiting process to show that a given knot can only be obtained in finitely many ways by adding twists to a suitably chosen ribbon. The resulting families of ribbons yield, even for relatively simple cases, ribbon surfaces for many knots in the knot tables.
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