A lower bound on the width of satellite knots
A lower bound on the width of satellite knots
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发表时间：
2010-08
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通讯作者：
Alexander Zupan
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作者：
Alexander Zupan
3-球面中节点的薄位置由Gabai引入，并已在各种上下文中使用。我们猜想一个类似的定理舒伯特和Schultens关于桥数的卫星节。对于一个卫星纽结K，我们利用伴环T给出了w（K）的一个下界，证明了K有一个2-桥伴环的猜想。作为一个推论，我们发现薄的位置，任何卫星结的编织模式和2桥同伴。
Thin position for knots in the 3-sphere was introduced by Gabai and has been used in a variety of contexts. We conjecture an analogue to a theorem of Schubert and Schultens concerning the bridge number of satellite knots. For a satellite knot K, we use the companion torus T to provide a lower bound for w(K), proving the conjecture for K with a 2-bridge companion. As a corollary, we find thin position for any satellite knot with a braid pattern and 2-bridge companion.