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Dissertation
Two varieties of tunnel number subadditivity
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Summer 2012
DOI: 10.17077/etd.fd0joa4z
Abstract
<p>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).</p>
Details
- Title: Subtitle
- Two varieties of tunnel number subadditivity
- Creators
- Trenton Frederick Schirmer - University of Iowa
- Contributors
- Maggy Tomova (Advisor)Charles Frohman (Committee Member)Jon Simon (Committee Member)Paul Muhly (Committee Member)Rodica Curtu (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Mathematics
- Date degree season
- Summer 2012
- Publisher
- University of Iowa
- DOI
- 10.17077/etd.fd0joa4z
- Number of pages
- vi, 49 pages
- Copyright
- Copyright 2012 Trenton Frederick Schirmer
- Language
- English
- Description illustrations
- charts
- Description bibliographic
- Includes bibliographical references (pages 47-49).
- Academic Unit
- Mathematics
- Record Identifier
- 9983777047702771
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