Osaka Journal of Mathematics

Determining the Hurwitz orbit of the standard generators of a braid group

Yoshiro Yaguchi

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Abstract

The Hurwitz action of the $n$-braid group $B_{n}$ on the $n$-fold product $(B_{m})^{n}$ of the $m$-braid group $B_{m}$ is studied. Using a natural action of $B_{n}$ on trees with $n$ labeled edges and $n+1$ labeled vertices, we determine all elements of the orbit of every $n$-tuple of the $n$ distinct standard generators of $B_{n+1}$ under the Hurwitz action of $B_{n}$.

Article information

Source
Osaka J. Math., Volume 52, Number 1 (2015), 59-71.

Dates
First available in Project Euclid: 24 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1427202872

Mathematical Reviews number (MathSciNet)
MR3326602

Zentralblatt MATH identifier
1328.20058

Subjects
Primary: 20F36: Braid groups; Artin groups
Secondary: 20F34: Fundamental groups and their automorphisms [See also 57M05, 57Sxx]

Citation

Yaguchi, Yoshiro. Determining the Hurwitz orbit of the standard generators of a braid group. Osaka J. Math. 52 (2015), no. 1, 59--71. https://projecteuclid.org/euclid.ojm/1427202872


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