On the degeneration of tunnel numbers under a connected sum (Q2787990)
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scientific article; zbMATH DE number 6550669
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the degeneration of tunnel numbers under a connected sum |
scientific article; zbMATH DE number 6550669 |
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On the degeneration of tunnel numbers under a connected sum (English)
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7 March 2016
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knots
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tunnel numbers
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meridionally primitive knots
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Investigating the tunnel numbers of summed knots, the authors give counterexamples to a conjecture of Morimoto and Moriah, proving that for any integer \(n\) greater than 2 there exists a prime knot \(k\) which is not meridionally primitive and has tunnel number equal to or greater than that of \(k\# k'\) for every \(m\)-bridge knot \(k'\) with \(m\) less than or equal to \(n\).
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