Ideal triangulation and disc unfolding of a singular flat surface

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dc.authoridSaglam, Ismail/0000-0002-1283-6396
dc.contributor.authorSaglam, Ismail
dc.date.accessioned2025-01-06T17:37:54Z
dc.date.available2025-01-06T17:37:54Z
dc.date.issued2021
dc.description.abstractAn ideal triangulation of a singular flat surface is a geodesic triangulation such that its vertex set is equal to the set of singular points of the surface. Using the fact that each pair of points in a surface has a finite number of geodesics having length <= L connecting them, where L is any positive number, we prove that each singular flat surface has an ideal triangulation provided that the surface has singular points when it has no boundary components, or each of its boundary components has a singular point. Also, we prove that such a surface contains a finite number of geodesics which connect its singular points so that when we cut the surface through these arcs we get a flat disc with a nonsingular interior.
dc.description.sponsorshipTUBITAK
dc.description.sponsorshipThe author is supported by TUBITAK. He is also grateful to Ahmet Refah Torun for his suggestions.
dc.identifier.doi10.3906/mat-2012-81
dc.identifier.endpage1648
dc.identifier.issn1300-0098
dc.identifier.issn1303-6149
dc.identifier.issue4
dc.identifier.scopus2-s2.0-85111475742
dc.identifier.scopusqualityQ2
dc.identifier.startpage1635
dc.identifier.trdizinid528455
dc.identifier.urihttps://doi.org/10.3906/mat-2012-81
dc.identifier.urihttps://search.trdizin.gov.tr/tr/yayin/detay/528455
dc.identifier.urihttps://hdl.handle.net/20.500.14669/2414
dc.identifier.volume45
dc.identifier.wosWOS:000678517500012
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.indekslendigikaynakTR-Dizin
dc.language.isoen
dc.publisherTubitak Scientific & Technological Research Council Turkey
dc.relation.ispartofTurkish Journal of Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241211
dc.subjectFlat surface
dc.subjectraw length spectrum
dc.subjectseparatrix
dc.subjectideal triangulation
dc.subjectunfolding
dc.subjectsaddle connection
dc.subjecttranslation surface
dc.titleIdeal triangulation and disc unfolding of a singular flat surface
dc.typeArticle

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