Equivalence of Cyclic p-squared Actions on Handlebodies

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 ( (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 ( (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. KCI Citation Count: 0