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University of Illinois at Urbana-Champaign
Enumeration and classification of ribbon knots
Abstract
dc:descriptionA 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.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2011
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Brown, Scott Allen
- Contributors dc:contributor
-
- Haken, Wolfgang
Subjects
dc:subject × 1Rights
dc:rights- Statement dc:rights
-
- Copyright 1995 Brown, Scott Allen
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
-
AAI9543541
(UMI)AAI9543541 - OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/22501