Abstract. In this paper we consider all orientation-preserving Z 4 -actions on 3-dimensional handlebodies Vg of genus g > 0. We study the graph of groups (Γ(v), G(v)), which determines a handlebody orbifold V (Γ(v), G(v)) ≃ Vg/Z 4 . This algebraic characterization is used to enumerate the total number of Z 4 group actions on such handlebodies, up to equivalence.
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