Equivalence of Z4-actions on Handlebodies of Genus g
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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$),\mathbf{G(v)})$, which determines a handlebody orbifold $V(\Gamma($v$),{\mathbf{G(v)}})\simeq{V_g}/\mathbb{Z}_{4}$. This algebraic characterization is used to enumerate the total number of $\mathbb{Z}_{4}$ group actions on such handlebodies, up to equivalence.
Abstract
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$),\mathbf{G(v)})$, which determines a handlebody orbifold $V(\Gamma($v$),{\mathbf{G(v)}})\simeq{V_g}/\mathbb{Z}_{4}$. This algebraic characterization is used to enumerate the total number of $\mathbb{Z}_{4}$ group actions on such handlebodies, up to equivalence.
참고문헌 (5)
- D. I. Fuchs-Rabinovitch, "On the automorphism group of free products", I, Mat. Sb., 8, pp.265~276 (1940)
- J. Kalliongis, "Equivalence and strong equivalence of actions on handle-bodies", Trans. Amer. Math. Soc., 308, pp.721~745 (1988)
- 김정수, "Structures of geometric quotient orbifolds of three-dimensional G-manifolds of genus two", 대한수학회지, 46(4), pp.859~893 (2009), 대한수학회
- D. McCullough, "Group actions on handlebodies", Proc. London Math. Soc., 59(3), pp.373~416 (1989)
- J. Prince-Lubawy, "Equivalence of cyclic p2-actions on handlebodies", ~