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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.

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On hyperbolic cobordisms and Hurwitz classes of holomorphic coverings
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by Carlos Cabrera, Peter Makienko and Guillermo Sienra PDF
Conform. Geom. Dyn. 23 (2019), 283-306 Request permission

Abstract:

In this article we show that for every collection $\mathcal {C}$ of an even number of polynomials, all of the same degree $d>2$ and in general position, there exist two hyperbolic $3$-orbifolds $M_1$ and $M_2$ with a Möbius morphism $\alpha :M_1\rightarrow M_2$ such that the restriction of $\alpha$ to the boundaries $\partial M_1$ and $\partial M_2$ forms a collection of maps $Q$ in the same conformal Hurwitz class of the initial collection $\mathcal {C}$. Also, we discuss the relationship between conformal Hurwitz classes of rational maps and classes of continuous isomorphisms of sandwich products on the set of rational maps.
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Additional Information
  • Carlos Cabrera
  • Affiliation: Instituto de Matematicas, Unidad Cuernavaca, University Nacional Autonoma de Mexico, Av Universidad s/n, Col Lomas de Chamilpa, 62210 Cuernavaca, MOR, Mexico
  • MR Author ID: 829036
  • Email: carloscabrerao@im.unam.mx
  • Peter Makienko
  • Affiliation: Instituto de Matematicas, Unidad Cuernavaca, University Nacional Autonoma de Mexico, Av Universidad s/n, Col Lomas de Chamilpa, 62210 Cuernavaca, MOR, Mexico
  • Email: makienko@im.unam.mx
  • Guillermo Sienra
  • Affiliation: Facultad de Ciencias, Universidad Nacional Autonoma De Mexico, Av. Universidad 3000, 04510 Mexico
  • MR Author ID: 223466
  • Email: gsl@dinamica1.fciencias.unam.mx
  • Received by editor(s): January 15, 2019
  • Received by editor(s) in revised form: October 25, 2019
  • Published electronically: December 13, 2019
  • Additional Notes: This work was partially supported by PAPIIT IN102515 and CONACYT CB15/255633.
  • © Copyright 2019 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 23 (2019), 283-306
  • MSC (2010): Primary 30F40, 32Q45, 37F30, 57M12
  • DOI: https://doi.org/10.1090/ecgd/345
  • MathSciNet review: 4042295