Growth rates of n-knots☆
Growth rates of n-knots☆
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n结生长率☆
DOI：
10.1016/0166-8641(91)90123-4
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发表时间：
1991
影响因子：
0.6
通讯作者：
D. Silver
中科院分区：
文献类型：
--
作者：
D. Silver
我们利用群自同态的增长率定义了一个不变量γκ，对于任何定向球面或圆盘结K，只要它的群有n-生成的换位子群。在纤维双曲1-knotK的特殊情况下，γκ是伪Anosov单值拉伸因子的对数。我们得到了关于卫星结的一些结果。我们证明了存在无穷多个不同的双切片纤维带状1-纽结具有相同的规定亚历山大多项式，我们给出了一个例子，一个不可逆的纤维带状2-纽结，满足Ruberman的必要条件，纤维偶数维纽结是可逆的。此外，我们提出了宫崎的论点，即γ尊重纤维1-节集上的带状和谐的偏序。
We use growth rates of group endomorphisms to define an invariant γκfor any oriented spherical or diskn-knotK, provided its group has finitely generated commutator subgroup. In the special case of a fibered hyperbolic 1-knotK, γκis the log of the stretching factor of the pseudo-Anosov monodromy. We obtain results about sateliten-knots. We prove that there exist infinitely many distinct doubly slice fibered ribbon 1-knots having the same prescribed Alexander polynomial, and we give an example of a noninvertible fibered ribbon 2-knot that satisfies Ruberman's necessary conditions for a fibered even-dimensional knot to be invertible. Also, we present Miyazaki's argument that γ respects the partial ordering of ribbon concordance on the set of fibered 1-knots.