Advisor

Steven A. Bleiler

Date of Award

1995

Document Type

Dissertation

Degree Name

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

Department

Systems Science

Physical Description

iv, 77 leaves: ill. 28 cm.

Subjects

Knot theory, Three-manifolds (Topology)

DOI

10.15760/etd.1272

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.

Description

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Persistent Identifier

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

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