• Title/Summary/Keyword: handlebody 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.

Equivalence of ℤ4-actions on Handlebodies of Genus g

  • Prince-Lubawy, Jesse
    • Kyungpook Mathematical Journal
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    • v.56 no.2
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    • pp.577-582
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    • 2016
  • In this paper we consider all orientation-preserving ${\mathbb{Z}}_4$-actions on 3-dimensional handlebodies $V_g$ of genus g > 0. We study the graph of groups (${\Gamma}(v)$, G(v)), which determines a handlebody orbifold $V({\Gamma}(v),G(v)){\simeq}V_g/{\mathbb{Z}}_4$. This algebraic characterization is used to enumerate the total number of ${\mathbb{Z}}_4$ group actions on such handlebodies, up to equivalence.