结点的Hopf交叉数最多为1

arXiv: Geometric Topology Pub Date : 2019-07-26 DOI:10.18910/75915

M. Mroczkowski

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引用次数: 3

摘要

考虑由$S^3$投影得到的$S^2$中的连杆图与Hopf映射以及这种图的最小交叉数。允许图最多有一个交叉点的结被分类。揭示了这些结的一些性质。特别地，我们确定了这些结中的哪些是代数的，并且对于这些结，给出了Fiedler提出的问题的答案。

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Knots with Hopf crossing number at most one

We consider diagrams of links in $S^2$ obtained by projection from $S^3$ with the Hopf map and the minimal crossing number for such diagrams. Knots admitting diagrams with at most one crossing are classified. Some properties of these knots are exhibited. In particular, we establish which of these knots are algebraic and, for such knots, give an answer to a problem posed by Fiedler.

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来源期刊

arXiv: Geometric Topology

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