Bridge Spectra of Twisted Torus Knots

Bridge Spectra of Twisted Torus Knots
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扭曲环面结的桥谱

DOI：
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发表时间：
2014
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通讯作者：
Alexander Zupan
Alexander Zupan
中科院分区：
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文献类型：
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作者：
R. S. Bowman;Scott A. Taylor;Alexander Zupan

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我们计算了一类充分泛型双曲扭曲环面结的零格桥数，并给出了零格桥数的下界。结果，这些结的桥谱有两个间隙，可以选择任意大，提供了第一个已知的双曲结具有这种性质的例子。此外，我们还证明了具有任意大一格桥数的Berge节和Dean节的存在，并由此给出了关于隧道一格桥数的Eudave-Mu~noz问题的解。
We compute the genus zero bridge numbers and give lower bounds on the genus one bridge numbers for a large class of sufficiently generic hyperbolic twisted torus knots. As a result, the bridge spectra of these knots have two gaps which can be chosen to be arbitrarily large, providing the first known examples of hyperbolic knots exhibiting this property. In addition, we show that there are Berge and Dean knots with arbitrarily large genus one bridge numbers, and as a result, we give solutions to problems of Eudave-Mu~noz concerning tunnel number one knots.