Triangulations and quadrangulations of the sphere

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Saglam I.

INTERNATIONAL JOURNAL OF MATHEMATICS, vol.26, no.8, 2015 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 26 Issue: 8
• Publication Date: 2015
• Doi Number: 10.1142/s0129167x15500639
• Journal Name: INTERNATIONAL JOURNAL OF MATHEMATICS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Galatasaray University Affiliated: No

Abstract

Thurston proved that the space of non-negatively curved triangulations of the 2-sphere can be parametrized by a quotient of a lattice by a group. We prove his result by a new method. Also we prove similar results for some different families of triangulations and quadrangulations of the 2-sphere.