Nonsimple, ribbon fibered knots
Nonsimple, ribbon fibered knots
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非简单的带状纤维结
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发表时间：
1994
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通讯作者：
Katura Miyazaki
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作者：
Katura Miyazaki
.一个任意纽结和它的镜像的连通和是一个丝带纽结，然而，匡威并不一定对所有的丝带纽结都成立。我们证明了匡威的任何带状纤维结，这是一个连接的总和迭代环面结，结不可约的亚历山大多项式，或电缆等结。这为非带状纤维节的检测提供了一种实用的方法。该证明使用了卡森和戈登通过单值性对同伦丝带、纤维结的表征。我们还研究了当索纤维结是带状时，结果支持下面的猜想。猜想如果一个纤维结k的（p，q）缆绳是带状的，其中p（> 1）是缆绳在Sx x D2中的绕数，则q = ± 1，k是带状的。
. The connected sum of an arbitrary knot and its mirror image is a rib-bon knot, however the converse is not necessarily true for all ribbon knots. We prove that the converse holds for any ribbon fibered knot which is a connected sum of iterated torus knots, knots with irreducible Alexander polynomials, or cables of such knots. This gives a practical method to detect nonribbon fibered knots. The proof uses a characterization of homotopically ribbon, fibered knots by their monodromies due to Casson and Gordon. We also study when cable fibered knots are ribbon and results which support the following conjecture. Conjecture. If a (p, q) cable of a fibered knot k is ribbon where p (> 1) is the winding number of a cable in Sx x D2 , then q = ± 1 and k is ribbon.