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Equivalence of ℤ4-actions on Handlebodies of Genus g
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  • Journal title : Kyungpook mathematical journal
  • Volume 56, Issue 2,  2016, pp.577-582
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2016.56.2.577
 Title & Authors
Equivalence of ℤ4-actions on Handlebodies of Genus g
Prince-Lubawy, Jesse;
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In this paper we consider all orientation-preserving -actions on 3-dimensional handlebodies of genus g > 0. We study the graph of groups (, G(v)), which determines a handlebody orbifold . This algebraic characterization is used to enumerate the total number of group actions on such handlebodies, up to equivalence.
handlebodies;orbifolds;graph of groups;orientation-preserving;cyclic actions;
 Cited by
D. I. Fuchs-Rabinovitch, On the automorphism group of free products, I, Mat. Sb., 8(1940), 265-276.

J. Kalliongis and A. Miller, Equivalence and strong equivalence of actions on handlebodies, Trans. Amer. Math. Soc., 308(1988), 721-745. crossref(new window)

J. Kim, Structures of geometric quotient orbifolds of three-dimensional g-manifolds of genus 2, J. Korean Math. Soc., 46(4)(2009), 859-893. crossref(new window)

D. McCullough, A. Miller, and B. Zimmerman, Group actions on handlebodies, Proc. London Math. Soc., 59(3)(1989), 373-416.

J. Prince-Lubawy, Equivalence of cyclic $p^2$-actions on handlebodies, In preparation.