Kyungpook Mathematical Journal

  • 제56권2호
  • /
  • Pages.577-582
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  • 2016
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Equivalence of ℤ4-actions on Handlebodies of Genus g

  • 투고 : 2015.02.25
  • 심사 : 2015.11.23
  • 발행 : 2016.06.23
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초록

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.

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참고문헌

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  2. J. Kalliongis and A. Miller, Equivalence and strong equivalence of actions on handlebodies, Trans. Amer. Math. Soc., 308(1988), 721-745. https://doi.org/10.1090/S0002-9947-1988-0951625-5
  3. J. Kim, Structures of geometric quotient orbifolds of three-dimensional g-manifolds of genus 2, J. Korean Math. Soc., 46(4)(2009), 859-893. https://doi.org/10.4134/JKMS.2009.46.4.859
  4. D. McCullough, A. Miller, and B. Zimmerman, Group actions on handlebodies, Proc. London Math. Soc., 59(3)(1989), 373-416.
  5. J. Prince-Lubawy, Equivalence of cyclic $p^2$-actions on handlebodies, In preparation.