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      저자 : Yasar Sozen (검색결과 4 건)
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      • SCIESCOPUSKCI등재

        IDEAL CELL-DECOMPOSITIONS FOR A HYPERBOLIC SURFACE AND EULER CHARACTERISTIC

        Sozen, Yasar Korean Mathematical Society 2008 대한수학회지 Vol.45 No.4

        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.

      • KCI등재

        Ideal cell-decompositions for a hyperbolic surface and Euler characteristic

        Yasar Sozen 대한수학회 2008 대한수학회지 Vol.45 No.4

        In this article, we constructively prove that on a surface S with genus g ≥ 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 celldecompositions. In this article, we constructively prove that on a surface S with genus g ≥ 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 celldecompositions.

      • SCIESCOPUSKCI등재

        REIDEMEISTER TORSION AND ORIENTABLE PUNCTURED SURFACES

        Dirican, Esma,Sozen, Yasar Korean Mathematical Society 2018 대한수학회지 Vol.55 No.4

        Let ${\Sigma}_{g,n,b}$ denote the orientable surface obtained from the closed orientable surface ${\Sigma}_g$ of genus $g{\geq}2$ by deleting the interior of $n{\geq}1$ distinct topological disks and $b{\geq}1$ points. Using the notion of symplectic chain complex, the present paper establishes a formula for computing Reidemeister torsion of the surface ${\Sigma}_{g,n,b}$ in terms of Reidemeister torsion of the closed surface ${\Sigma}_g$, Reidemeister torsion of disk, and Reidemeister torsion of punctured disk.

      • KCI등재

        Reidemeister torsion and orientable punctured surfaces

        Esma Dirican,Yasar Sozen 대한수학회 2018 대한수학회지 Vol.55 No.4

        Let $\Sigma_{g,n,b}$ denote the orientable surface obtained from the closed orientable surface $\Sigma_g$ of genus $g\geq2$ by deleting the interior of $n\geq 1$ distinct topological disks and $b\geq 1$ points. Using the notion of symplectic chain complex, the present paper establishes a formula for computing Reidemeister torsion of the surface $\Sigma_{g,n,b}$ in terms of Reidemeister torsion of the closed surface $\Sigma_{g},$ Reidemeister torsion of disk, and Reidemeister torsion of punctured disk.

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