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...
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| Format: | Others |
| Language: | English |
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University of Iowa
2012
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| Online Access: | https://ir.uiowa.edu/etd/3379 https://ir.uiowa.edu/cgi/viewcontent.cgi?article=3324&context=etd |
| Summary: | 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). |
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