On the braid index of a two-bridge knot (Q6590037)
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scientific article; zbMATH DE number 7899103
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the braid index of a two-bridge knot |
scientific article; zbMATH DE number 7899103 |
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On the braid index of a two-bridge knot (English)
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21 August 2024
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Two-bridge knots are an important class of knots which correspond to rational numbers. In this paper, the authors consider the braid indices of two-bridge knots.\N\NFirst they prove an inequality on the braid indices of two-bridge knots if there exists an epimorphism between their knot groups. Then they determine the minimality of two-bridge knots with small braid index by analyzing the above inequality carefully. Finally, they compute the average ``sign change'', then the average braid index of all the two-bridge knots with a given crossing number using some subtle combinatorial identities.
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braid index
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crossing number
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epimorphism
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minimal knot
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two-bridge knot
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