Osaka Journal of Mathematics

Knots with Hopf crossing number at most one

Maciej Mroczkowski

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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 in [3].

Article information

Osaka J. Math., Volume 57, Number 2 (2020), 279-304.

First available in Project Euclid: 6 April 2020

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds


Mroczkowski, Maciej. Knots with Hopf crossing number at most one. Osaka J. Math. 57 (2020), no. 2, 279--304.

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