## Osaka Journal of Mathematics

### Knots with Hopf crossing number at most one

Maciej Mroczkowski

#### Abstract

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

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

Dates
First available in Project Euclid: 6 April 2020

https://projecteuclid.org/euclid.ojm/1586160079

Mathematical Reviews number (MathSciNet)
MR4081733

Zentralblatt MATH identifier
07196679

#### Citation

Mroczkowski, Maciej. Knots with Hopf crossing number at most one. Osaka J. Math. 57 (2020), no. 2, 279--304. https://projecteuclid.org/euclid.ojm/1586160079

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