Nielsen equivalence in mapping tori over the torus
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- by Ian Biringer
- Conform. Geom. Dyn. 21 (2017), 105-110
- DOI: https://doi.org/10.1090/ecgd/308
- Published electronically: March 13, 2017
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Abstract:
We use the geometry of the Farey graph to give an alternative proof of the fact that if $A \in GL_2\mathbb {Z}$ and if $G_A=\mathbb {Z}^2 \rtimes _A \mathbb {Z}$ is generated by two elements, then there is a single Nielsen equivalence class of $2$-element generating sets for $G_A$ unless $A$ is conjugate to $\pm \left (\begin {smallmatrix} 2 & 1 \\ 1 & 1 \end {smallmatrix}\right )$, in which case there are two.References
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Bibliographic Information
- Ian Biringer
- Affiliation: Boston College, Department of Mathematics, 140 Commonwealth Ave, Chestnut Hill, MA 02467
- Email: ianbiringer@gmail.com
- Received by editor(s): October 27, 2016
- Received by editor(s) in revised form: February 23, 2017
- Published electronically: March 13, 2017
- Additional Notes: The author was partially supported by NSF grant DMS 1611851
- © Copyright 2017 American Mathematical Society
- Journal: Conform. Geom. Dyn. 21 (2017), 105-110
- MSC (2010): Primary 57M07
- DOI: https://doi.org/10.1090/ecgd/308
- MathSciNet review: 3622115