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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Nielsen equivalence in mapping tori over the torus
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by Ian Biringer PDF
Conform. Geom. Dyn. 21 (2017), 105-110 Request permission


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.
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Additional Information
  • Ian Biringer
  • Affiliation: Boston College, Department of Mathematics, 140 Commonwealth Ave, Chestnut Hill, MA 02467
  • Email:
  • 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:
  • MathSciNet review: 3622115