On hyperbolic cobordisms and Hurwitz classes of holomorphic coverings
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- by Carlos Cabrera, Peter Makienko and Guillermo Sienra
- Conform. Geom. Dyn. 23 (2019), 283-306
- DOI: https://doi.org/10.1090/ecgd/345
- Published electronically: December 13, 2019
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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
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Bibliographic 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