Properties of knots preserved by cabling
Properties of knots preserved by cabling
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DOI：
10.4310/cag.2011.v19.n3.a4
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发表时间：
2010-10
期刊：
影响因子：
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通讯作者：
Alexander Zupan
中科院分区：
文献类型：
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作者：
Alexander Zupan
我们研究结J的几何性质，这些性质通过取J的（p，q）-电缆K而不变。具体地说，我们将w（K）与w（J）联系起来，其中w（K）是K在Gabai意义上的宽度。我们使用这些信息来证明薄位置是J的最小桥位置当且仅当K也是如此，并且更一般地，我们证明K的任何薄位置是J的薄位置的“明显”布线。我们通过证明J是极小的来得出结论（mp-small）当且仅当K是极小的（mp-small），并且如果J是mp-small并且J的每个非极小桥位置是稳定的，则对于K也是如此。
We examine geometric properties of a knot J that are unchanged by taking a (p,q)-cable K of J. Specifically, we relate w(K) to w(J), where w(K) is the width of K in the sense of Gabai. We use this information to demonstrate that thin position is a minimal bridge position of J if and only if the same is true for K, and more generally we show that any thin position of K is an "obvious" cabling of a thin position of J. We conclude by proving that J is meridionally small (mp-small) if and only if K is meridionally small (mp-small), and if J is mp-small and every non-minimal bridge position of J is stabilized, then the same is true for K.