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IDEAL CELL-DECOMPOSITIONS FOR A HYPERBOLIC SURFACE AND EULER CHARACTERISTIC
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 Title & Authors
IDEAL CELL-DECOMPOSITIONS FOR A HYPERBOLIC SURFACE AND EULER CHARACTERISTIC
Sozen, Yasar;
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 Abstract
In this article, we constructively prove that on a surface S with genus g2, there exit maximal geodesic laminations with 7g-7,...,9g-9 leaves. Thus, S can have ideal cell-decompositions (i.e., S can be (ideally) triangulated by maximal geodesic laminations) with 7g-7,...,9g-9 (ideal) 1-cells. Once there is a triangulation for a compact surface, the Euler characteristic for the surface can be calculated as the alternating sum F-E+V, where F, E, and V denote the number of faces, edges, and vertices, respectively. We also prove that the same formula holds for the ideal cell decompositions.
 Keywords
ideal cell-decomposition;geodesic lamination;Euler characteristic;
 Language
English
 Cited by
 References
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