Equivalence of ℤ4-actions on Handlebodies of Genus g

• Journal title : Kyungpook mathematical journal
• Volume 56, Issue 2,  2016, pp.577-582
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2016.56.2.577
Title & Authors
Equivalence of ℤ4-actions on Handlebodies of Genus g
Prince-Lubawy, Jesse;

Abstract
In this paper we consider all orientation-preserving $\small{{\mathbb{Z}}_4}$-actions on 3-dimensional handlebodies $\small{V_g}$ of genus g > 0. We study the graph of groups ($\small{{\Gamma}(v)}$, G(v)), which determines a handlebody orbifold $\small{V({\Gamma}(v),G(v)){\simeq}V_g/{\mathbb{Z}}_4}$. This algebraic characterization is used to enumerate the total number of $\small{{\mathbb{Z}}_4}$ group actions on such handlebodies, up to equivalence.
Keywords
handlebodies;orbifolds;graph of groups;orientation-preserving;cyclic actions;
Language
English
Cited by
References
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