Morimoto--Sakuma--Yokota's geometric approach to tunnel number one knots (Q1868864)
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scientific article; zbMATH DE number 1901912
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Morimoto--Sakuma--Yokota's geometric approach to tunnel number one knots |
scientific article; zbMATH DE number 1901912 |
Statements
Morimoto--Sakuma--Yokota's geometric approach to tunnel number one knots (English)
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28 April 2003
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The author introduces the concept of characteristic knots to \(\theta\)-curves with bridge decompositions. For a given knot \(K\) in \(S^3\), a tunnel is defined as an embedded arc in \(S^3\) with endpoints on \(K\) and interior disjoint from \(K\). A knot with an unknotting tunnel is called a tunnel-1 knot. By means of the refinement of Morimoto-Sakuma-Yokota's method of studying tunnel number one knots, another proof is provided for the tunnel number of the Montesinos knots dealt with by Klimenko-Sakuma.
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Tunnel number one knot
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\(\theta\)-curve
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\({\mathbb Z}_2 \oplus {\mathbb Z}_2\)-branched covering
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Heegaard decomposition
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Montesinos knots
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0.8913317
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0.88068074
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0.8542597
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0.84480774
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0.84026194
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0.8391202
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0.8384545
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0.8363291
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