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arXiv · 1509.06688

Equivalence of $\mathbb{Z}_{4}$-actions on handlebodies of genus $g$

Jesse Prince-Lubawy
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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 $(Γ($v$),\mathbf{G(v)})$, which determines a handlebody orbifold $V(Γ($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.

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BibTeXRIS

Jesse Prince-Lubawy. 2015-09-22. Equivalence of $\mathbb{Z}_{4}$-actions on handlebodies of genus $g$. https://doi.org/10.5666/kmj.2016.56.2.577

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