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Two varieties of tunnel number subadditivity

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).

Identiferoai:union.ndltd.org:uiowa.edu/oai:ir.uiowa.edu:etd-3324
Date01 July 2012
CreatorsSchirmer, Trenton Frederick
ContributorsTomova, Maggy
PublisherUniversity of Iowa
Source SetsUniversity of Iowa
LanguageEnglish
Detected LanguageEnglish
Typedissertation
Formatapplication/pdf
SourceTheses and Dissertations
RightsCopyright 2012 Trenton Frederick Schirmer

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