Equivalence of Cyclic p-squared Actions on Handlebodies
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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.
Abstract
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.
참고문헌 (4)
- D. I. Fuchs-Rabinovitch, "On the automorphism group of free products", I, Mat. Sb, 8, pp.265~276 (1940)
- J. Kalliongis, "Equivalence and strong equivalence of actions on handle-bodies", Trans. Amer. Math. Soc, 308(2), pp.721~745 (1988)
- D. McCullough, "Group actions on handlebodies", Proc. London Math. Soc, 59(3), pp.373~416 (1989)
- Jesse Prince-Lubawy, "Equivalence of Z4-actions on Handlebodies of Genus g", Kyungpook Mathematical Journal, 56(2), pp.577~582 (2016), 경북대학교 자연과학대학 수학과