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Fenchel’s conjecture on NEC groups

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dc.contributor.authorBujalance García, Emilio
dc.contributor.authorCirre Torres, Francisco Javier
dc.contributor.authorConder, Marston D. E.
dc.contributor.authorCosta González, Antonio Félix
dc.contributor.funderAgencia Estatal de Investigación
dc.date.accessioned2025-08-20T11:18:41Z
dc.date.available2025-08-20T11:18:41Z
dc.date.issued2025-08-20
dc.descriptionThe registered version of this article, first published in “Revista Matemática Complutense, 2025", is available online at the publisher's website: Springer Nature, https://doi.org/10.1007/s13163-025-00540-w La versión registrada de este artículo, publicado por primera vez en “Revista Matemática Complutense, 2025", está disponible en línea en el sitio web del editor: Springer Nature, https://doi.org/10.1007/s13163-025-00540-w
dc.description.abstractA classical discovery known as Fenchel's conjecture and proved in the 1950s, shows that every co-compact Fuchsian group has a normal subgroup of finite index isomorphic to the fundamental group of a compact unbordered orientable surface, or in algebraic terms, that has a normal subgroup of finite index that contains no element of finite order other than the identity. In this paper we initiate and make progress on an extension of Fenchel's conjecture by considering the following question: Does every planar non-Euclidean crystallographic group containing transformations that reverse orientation have a normal subgroup of finite index isomorphic to the fundamental group of a compact unbordered non-orientable surface? We answer this question in the affirmative in the case where the orbit space of is a nonorientable surface, and also in the case where this orbit space is a bordered orientable surface of positive genus. In the case where the genus of the quotient is , we have an affirmative answer in many subcases, but the question is still open for others.en
dc.description.versionversión final
dc.identifier.citationEmilio Bujalance, F. Javier Cirre, Marston D. E. Conder, Antonio F. Costa (2025). Fenchel’s conjecture on NEC groups. Revista Matemática Complutense. https://doi.org/10.1007/s13163-025-00540-w
dc.identifier.doihttps://doi.org/10.1007/s13163-025-00540-w
dc.identifier.issn1139-1138 | eISSN 1988-2807
dc.identifier.urihttps://hdl.handle.net/20.500.14468/29917
dc.journal.titleRevista Matemática Complutense
dc.language.isoen
dc.publisherSpringer
dc.relation.centerFacultad de Ciencias
dc.relation.departmentMatemáticas Fundamentales
dc.relation.projectidinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2023-152822NB-I00/ES/SUPERFICIES DE RIEMANN: SIMETRIA, SUPERSIMETRIA Y APLICACIONES
dc.rightsinfo:eu-repo/semantics/embargoedAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject12 Matemáticas
dc.titleFenchel’s conjecture on NEC groupsen
dc.typejournal articleen
dspace.entity.typePublication
relation.isAuthorOfPublication1772da05-48c6-45eb-b4ab-0dd9a36ea3b7
relation.isAuthorOfPublication3a744098-2ed6-40e8-90e1-33197c605cc2
relation.isAuthorOfPublication8dbf4941-94eb-4e49-a01e-8b9c32463231
relation.isAuthorOfPublication.latestForDiscovery1772da05-48c6-45eb-b4ab-0dd9a36ea3b7
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