Document Type

Dissertation

Date of Degree

Summer 2012

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Maggy Tomova

Abstract

Knot theory and 3-manifold topology are closely intertwined, and few invariants stand so firmly in the intersection of these two subjects as the tunnel number of a knot, denoted t(K). We describe two very general constructions that result in knot and link pairs which are subbaditive with respect to tunnel number under connect sum. Our constructions encompass all previously known examples and introduce many new ones. As an application we describe a class of knots K in the 3-sphere such that, for every manifold M obtained from an integral Dehn filling of E(K), g(E(K))>g(M).

Keywords

3-Manifolds, Heegaard splittings, Knots, Topology, Tunnel Number

Pages

vi, 49 pages

Bibliography

Includes bibliographical references (pages 47-49).

Copyright

Copyright 2012 Trenton Frederick Schirmer

Included in

Mathematics Commons

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