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Knots with Hopf crossing number at most one. (English) Zbl 1437.57011

Summary: 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 T. Fiedler in [Topology 30, No. 2, 259–265 (1991; Zbl 0725.57002)].

MSC:

57K10 Knot theory

Citations:

Zbl 0725.57002

Software:

KnotPlot; KnotInfo
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Full Text: arXiv Euclid

References:

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