Date of Degree
2012
Document Type
dissertation
Degree Name
PhD (Doctor of Philosophy)
Department
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).
Pages
vi, 49
Bibliography
47-49
Copyright
Copyright 2012 Trenton Frederick Schirmer
Recommended Citation
Schirmer, Trenton Frederick. "Two varieties of tunnel number subadditivity." dissertation, University of Iowa, 2012.
http://ir.uiowa.edu/etd/3379.