Ideal triangulation and disc unfolding of a singular flat surface
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Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Tubitak Scientific & Technological Research Council Turkey
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
An 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.
Açıklama
Anahtar Kelimeler
Flat surface, raw length spectrum, separatrix, ideal triangulation, unfolding, saddle connection, translation surface
Kaynak
Turkish Journal of Mathematics
WoS Q Değeri
Q3
Scopus Q Değeri
Q2
Cilt
45
Sayı
4