• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권1호
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• pp.91-99
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• 2015

A normal surface is determined by how the surface under consideration meets each tetrahedron in a given triangulation. We call such a nice embedded disk, which is a component of the intersection of the surface with a tetrahedron, an elementary disk. We classify all elementary disk types in a truncated ideal triangulation.

• 호남수학학술지
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• 제27권2호
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• pp.287-300
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• 2005

In this paper, we classify all taut structures for ideal triangulations with two and three tetrahedra.

• 대한수학회지
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• 제45권4호
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• pp.965-976
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• 2008

In this article, we constructively prove that on a surface S with genus g$\geq$2, 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.