The π-geography problem and the Hurwitz problem
| dc.citation.epage | 122 | |
| dc.citation.issue | 9 | |
| dc.citation.journalAbbreviatedTitle | ing.cienc. | eng |
| dc.citation.journalTitle | Ingeniería y Ciencia | eng |
| dc.citation.spage | 91 | |
| dc.citation.volume | 5 | |
| dc.contributor.affiliation | Universidad EAFIT | spa |
| dc.contributor.affiliation | Universidad Nacional de Colombia, Medellín | spa |
| dc.contributor.author | Cadavid, Carlos | spa |
| dc.contributor.author | Vélez-C.,Juan D. | spa |
| dc.coverage.spatial | Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees | eng |
| dc.date | 2009-06-01 | |
| dc.date.accessioned | 2019-11-22T19:06:22Z | |
| dc.date.available | 2019-11-22T19:06:22Z | |
| dc.date.issued | 2009-06-01 | |
| dc.description | Let d ≥ 2 be an integer and a partition of d. In this article we study the problem of for which pairs of integers (a, b) there is a branched coating F: ∑ → D2 = {z ∈ C: | z | 6 ≤ 1} that has critical values, x (∑) = −b, and such that the monodromy that is obtained when crossing the border of D2 in a positive sense belongs to the conjugation class in the symmetric group Sd determined by the π partition. Four variants of this problem are studied: i) without requiring domain connection, ii) requiring domain connection, iii) without requiring domain connection, but requiring that the coating be semi-stable, iv) requiring that the domain be related and that the coating is semi-stable. Complete solutions of the first two variants are obtained, and a partial solution of the remaining variants is obtained. It also explains how the interest in these problems arises from the study of an analogous question for functions whose domain is 4-dimensional. | eng |
| dc.description | Sea d ≥ 2 un entero y una partición de d. En este artículo se estudia el problema de para qué pares de enteros (a, b) existe un recubrimiento ramificado F : ∑ → D2 = {z ∈ C : |z| 6 ≤ 1} que tenga a valores críticos, x(∑) = −b, y tal que la monodromía que se obtiene cuando se recorre la frontera de D2 en sentido positivo pertenece a la clase de conjugancia en el grupo simétrico Sd determinada por la partición π. Se estudian cuatro variantes de este problema: i) sin requerir conexidad del dominio, ii) requiriendo conexidad del dominio, iii) sin requerir conexidad del dominio, pero exigiendo que el recubrimiento sea semiestable, iv) requiriendo que el dominio sea conexo y que el recubrimiento sea semiestable. Se obtienen soluciones completas de las primeras dos variantes, y se obtiene una solución parcial de las variantes restantes. Además se explica cómo el interés por estos problemas surge del estudio de una pregunta análoga para funciones cuyo dominio es 4-dimensional. | spa |
| dc.format | application/pdf | |
| dc.identifier.issn | 2256-4314 | |
| dc.identifier.issn | 1794-9165 | |
| dc.identifier.uri | http://hdl.handle.net/10784/14512 | |
| dc.language.iso | spa | spa |
| dc.publisher | Universidad EAFIT | spa |
| dc.relation.isversionof | http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/469 | |
| dc.relation.uri | http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/469 | |
| dc.rights | Copyright (c) 2009 Carlos Cadavid, Juan D. Vélez-C. | eng |
| dc.rights.accessrights | info:eu-repo/semantics/openAccess | eng |
| dc.rights.local | Acceso abierto | spa |
| dc.source | instname:Universidad EAFIT | |
| dc.source | reponame:Repositorio Institucional Universidad EAFIT | |
| dc.source | Ingeniería y Ciencia; Vol 5, No 9 (2009) | spa |
| dc.subject.keyword | Branched Coating | eng |
| dc.subject.keyword | Critical Value | eng |
| dc.subject.keyword | Characteristic Of Euler | eng |
| dc.subject.keyword | Riemann – Hurwitz Formula | eng |
| dc.subject.keyword | Hurwitz Problem | eng |
| dc.subject.keyword | Monodromia | eng |
| dc.subject.keyword | Recubrimiento Ramificado | spa |
| dc.subject.keyword | Valor Crítico | spa |
| dc.subject.keyword | Característica De Euler | spa |
| dc.subject.keyword | Fórmula De Riemann–Hurwitz | spa |
| dc.subject.keyword | Hurwitz Problem | spa |
| dc.subject.keyword | Monodromía | spa |
| dc.title | The π-geography problem and the Hurwitz problem | eng |
| dc.title | El problema de π-geografía y el problema de Hurwitz | spa |
| dc.type | article | eng |
| dc.type | info:eu-repo/semantics/article | eng |
| dc.type | publishedVersion | eng |
| dc.type | info:eu-repo/semantics/publishedVersion | eng |
| dc.type.local | Artículo | spa |