First Advisor

Steven A. Bleiler

Date of Publication

1995

Document Type

Dissertation

Degree Name

Doctor of Philosophy (Ph.D.) in Systems Science

Department

Systems Science

Language

English

Subjects

Knot theory, Three-manifolds (Topology)

DOI

10.15760/etd.1272

Physical Description

iv, 77 leaves: ill. 28 cm.

Abstract

In 1984, T. Kobayashi gave a classification of the genus two 3-manifolds with a nontrivial torus decomposition. The intent of this study is to extend this classification to the genus two, torally bounded 3-manifolds with a separating non-trivial torus decomposition. These 3-manifolds are also known as the tunnel-1 generalized satellite knot exteriors. The main result of the study is a full decomposition of the exterior of a tunnel-1 satellite knot in an arbitrary 3-manifold. Several corollaries are drawn from this classification. First, Schubert's 1953 results regarding the existence and uniqueness of a core component for satellite knots in the 3-sphere is extended to tunnel-1 satellite knots in arbitrary 3-manifolds. Second, Morimoto and Sakuma's 1991 classification of tunnel-1 satellite knots in the 3-sphere is extended to a classification of the tunnel-1 satellite knots in lens spaces. Finally, for these knot exteriors, a result of Eudave-Muñoz in 1994 regarding the relative position of tunnels and decomposing tori is recovered.

Rights

In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).

Comments

If you are the rightful copyright holder of this dissertation or thesis and wish to have it removed from the Open Access Collection, please submit a request to pdxscholar@pdx.edu and include clear identification of the work, preferably with URL

Persistent Identifier

http://archives.pdx.edu/ds/psu/4319

Download

Share

COinS