## Illinois Journal of Mathematics

### The braid index of surface-knots and quandle colorings

Kokoro Tanaka

#### Abstract

The braid index of a surface-knot $F$ is the minimal number among the degrees of all simple surface braids whose closures are ambient isotopic to $F$. We prove that there exists a surface-knot with braid index $k$ for any positive integer $k$. To prove it, we use colorings of surface-knots by quandles and give lower bounds of the braid index of surface-knots.

#### Article information

Source
Illinois J. Math., Volume 49, Number 2 (2005), 517-522.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138031

Digital Object Identifier
doi:10.1215/ijm/1258138031

Mathematical Reviews number (MathSciNet)
MR2164349

Zentralblatt MATH identifier
1077.57022

#### Citation

Tanaka, Kokoro. The braid index of surface-knots and quandle colorings. Illinois J. Math. 49 (2005), no. 2, 517--522. doi:10.1215/ijm/1258138031. https://projecteuclid.org/euclid.ijm/1258138031