Equivalence of cyclic p-squared actions on handlebodies

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© Kyungpook Mathematical Journal. In this paper we consider all orientation-preserving ℤp2 -actions on 3- dimensional handlebodies Vg of genus g > 0 for p an odd prime. To do so, we examine particular graphs of groups (Γ(v);G(v)) in canonical form for some 5-tuple v = (r,s,t,m,n) with r + s + t + m > 0. These graphs of groups correspond to the handlebody orbifolds V (Γ(v),G(v)) that are homeomorphic to the quotient spaces Vg / ℤp2 of genus less than or equal to g. This algebraic characterization is used to enumerate the total number of ℤp2 -actions on such handlebodies, up to equivalence.

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Kyungpook Mathematical Journal

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