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Title:Enumeration and classification of ribbon knots
Author(s):Brown, Scott Allen
Doctoral Committee Chair(s):Haken, Wolfgang
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
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.
Issue Date:1995
Type:Text
Language:English
URI:http://hdl.handle.net/2142/22501
Rights Information:Copyright 1995 Brown, Scott Allen
Date Available in IDEALS:2011-05-07
Identifier in Online Catalog:AAI9543541
OCLC Identifier:(UMI)AAI9543541


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