Remote Access Conformal Geometry and Dynamics
Green Open Access

Conformal Geometry and Dynamics

ISSN 1088-4173

 
 

 

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
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2010): 30F40, 32Q45, 37F30, 57M12

Retrieve articles in all journals with MSC (2010): 30F40, 32Q45, 37F30, 57M12


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.
Article copyright: © Copyright 2019 American Mathematical Society