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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

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.


Structural properties of quotient surfaces of a Hecke group
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by K. Farooq
Conform. Geom. Dyn. 23 (2019), 262-282
Published electronically: December 3, 2019


We study the properties of the surface $\Sigma _q$, which is a $2q$-fold cover of $\mathbb H/G_q$, where $G_q$ is a Hecke group and $q$ is an integer greater than $3$. We have slightly different situations for the even and odd values of $q$. For odd values of $q$ the surface $\Sigma _q$ is a $\frac {q-1}{2}$ genus surface with a cusp, whereas, for even values it is a $\frac {q-2}{2}$ genus surface with two cusps. We prove that there exist $g$ embedded tori with a hole on $\Sigma _q$, where $g=\frac {q-1}{2}$ when $q$ is an odd integer and $g=\frac {q-2}{2}$ when $q$ is even, with $g$ boundary geodesics at different heights. These boundary geodesics are the separating geodesics intersecting each other transversally. We also prove that the surface $\Sigma _q$ is a hyper-elliptic surface for every integer $q>3$.
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Bibliographic Information
  • K. Farooq
  • Affiliation: WMI, Univesity of Warwick, Coventry, CV4 7AL, United Kingdom
  • Address at time of publication: Department of Sciences and Humanities, National University of Emerging Sciences, FAST, A.K. Brohi Road, H-11/4, Islamabad, Pakistan
  • Email:
  • Received by editor(s): September 4, 2014
  • Received by editor(s) in revised form: July 26, 2017, and July 13, 2019
  • Published electronically: December 3, 2019
  • Additional Notes: The author was supported by WPRS grant from the University of Warwick, and HEC Partial Support by the Government of Pakistan
  • © Copyright 2019 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 23 (2019), 262-282
  • MSC (2010): Primary 20H10, 30B70, 57M50; Secondary 11K60
  • DOI:
  • MathSciNet review: 4038021