Date of Degree
PhD (Doctor of Philosophy)
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).
3-Manifolds, Heegaard splittings, Knots, Topology, Tunnel Number
vi, 49 pages
Includes bibliographical references (pages 47-49).
Copyright 2012 Trenton Frederick Schirmer