## Osaka Journal of Mathematics

### Pseudo diagrams of knots, links and spatial graphs

Ryo Hanaki

#### Abstract

A pseudo diagram of a spatial graph is a spatial graph projection on the $2$-sphere with over/under information at some of the double points. We introduce the trivializing (resp. knotting) number of a spatial graph projection by using its pseudo diagrams as the minimum number of the crossings whose over/under information lead the triviality (resp. nontriviality) of the spatial graph. We determine the set of non-negative integers which can be realized by the trivializing (resp. knotting) numbers of knot and link projections, and characterize the projections which have a specific value of the trivializing (resp. knotting) number.

#### Article information

Source
Osaka J. Math., Volume 47, Number 3 (2010), 863-883.

Dates
First available in Project Euclid: 24 September 2010

https://projecteuclid.org/euclid.ojm/1285334478

Mathematical Reviews number (MathSciNet)
MR2768805

Zentralblatt MATH identifier
1219.57006

#### Citation

Hanaki, Ryo. Pseudo diagrams of knots, links and spatial graphs. Osaka J. Math. 47 (2010), no. 3, 863--883. https://projecteuclid.org/euclid.ojm/1285334478

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