论文标题
在HOPF纤维化下的两个交叉数量的代数结上
On two crossing numbers of algebraic knots under Hopf fibration
论文作者
论文摘要
我们回答了守卫者在[1]中提出的一个问题，即在Hopf纤维化下的代数结$ k $的两个交叉数字概念，一个拓扑，表示$ h（k）$，另一个来自于围绕复杂奇异性的结意见，表示$ C_ {alg}（k）$。我们表明$ c_ {alg}（k）-h（k）$可以任意大。我们还为某些结的家庭提供了上限，例如Torus结$ t（2，n）$，扭曲结及其镜像。
We answer a question posed by Fielder in [1] concerning two notions of crossing number for algebraic knots $K$ under Hopf fibration, one topological, denoted $h(K)$, the other coming from the realization of such knots around complex singularities, denoted $C_{alg}(K)$. We show that $C_{alg}(K)-h(K)$ can be arbitrarily large. We also give an upper bound for $h$ of some families of knots such as torus knots $T(2,n)$, twist knots and their mirror images.
