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Conformal Geometry and Dynamics

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On hyperbolic cobordisms and Hurwitz classes of holomorphic coverings


Authors: Carlos Cabrera, Peter Makienko and Guillermo Sienra
Journal: Conform. Geom. Dyn. 23 (2019), 283-306
MSC (2010): Primary 30F40, 32Q45, 37F30, 57M12
DOI: https://doi.org/10.1090/ecgd/345
Published electronically: December 13, 2019
MathSciNet review: 4042295
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Abstract | References | Similar Articles | Additional Information

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
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
Email: gsl@dinamica1.fciencias.unam.mx

DOI: https://doi.org/10.1090/ecgd/345
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.
Article copyright: © Copyright 2019 American Mathematical Society