Ideal triangulation and disc unfolding of a singular flat surface

[ X ]

Tarih

2021

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

Künye