• Title/Summary/Keyword: hyperbolic orbifold

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STRUCTURES OF GEOMETRIC QUOTIENT ORBIFOLDS OF THREE-DIMENSIONAL G-MANIFOLDS OF GENUS TWO

  • Kim, Jung-Soo
    • Journal of the Korean Mathematical Society
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    • v.46 no.4
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    • pp.859-893
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    • 2009
  • In this article, we will characterize structures of geometric quotient orbifolds of G-manifold of genus two where G is a finite group of orientation preserving diffeomorphisms using the idea of handlebody orbifolds. By using the characterization, we will deduce the candidates of possible non-hyperbolic geometric quotient orbifolds case by case using W. Dunbar's work. In addition, if the G-manifold is compact, closed and the quotient orbifold's geometry is hyperbolic then we can show that the fundamental group of the quotient orbifold cannot be in the class D.

A GEOMETRIC REALIZATION OF (7/3)-RATIONAL KNOT

  • D.A.Derevnin;Kim, Yang-Kok
    • Communications of the Korean Mathematical Society
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    • v.13 no.2
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    • pp.345-358
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    • 1998
  • Let (p/q,n) denote the orbifold with its underlying space $S^3$ and a rational knot or link p/q as its singular set with a cyclic isotropy group of order n. In this paper we shall show the geometrical realization for the case (7/3,n) for all $n \geq 3$.

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The deformation space of real projective structures on the $(^*n_1n_2n_3n_4)$-orbifold

  • Lee, Jungkeun
    • Bulletin of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.549-560
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    • 1997
  • For positive integers $n_i \geq 2, i = 1, 2, 3, 4$, such that $\Sigma \frac{n_i}{1} < 2$, there exists a quadrilateral $P = P_1 P_2 P_3 P_4$ in the hyperbolic plane $H^2$ with the interior angle $\frac{n_i}{\pi}$ at $P_i$. Let $\Gamma \subset Isom(H^2)$ be the (discrete) group generated by reflections in each side of $P$. Then the quotient space $H^2/\gamma$ is a differentiable orbifold of type $(^* n_1 n_2 n_3 n_4)$. It will be shown that the deformation space of $Rp^2$-structures on this orbifold can be mapped continuously and bijectively onto the cell of dimension 4 - \left$\mid$ {i$\mid$n_i = 2} \right$\mid$$.

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SOME HYPERBOLIC SPACE FORMS WITH FEW GENERATED FUNDAMENTAL GROUPS

  • Cavicchioli, Alberto;Molnar, Emil;Telloni, Agnese I.
    • Journal of the Korean Mathematical Society
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    • v.50 no.2
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    • pp.425-444
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    • 2013
  • We construct some hyperbolic hyperelliptic space forms whose fundamental groups are generated by only two or three isometries. Each occurring group is obtained from a supergroup, which is an extended Coxeter group generated by plane re ections and half-turns. Then we describe covering properties and determine the isometry groups of the constructed manifolds. Furthermore, we give an explicit construction of space form of the second smallest volume nonorientable hyperbolic 3-manifold with one cusp.